Final Project
Ali Thursland and Mary Helen Wood
11/20/2018
#Read file
airbnb <- read.csv("https://raw.githubusercontent.com/athursland/STA-210/master/airbnb.csv?fbclid=IwAR0ffZSvoMPWxJjX-a4gWp2UlripEqAK0NJtu2ioHgmG0uWjCm20Hse8pNw")Data Preparation
#Make new variable has_reviews
airbnb <- airbnb %>%
mutate(has_reviews = case_when(
number_of_reviews == 0 ~ 0,
number_of_reviews > 0 ~ 1)
)
#Make NAs = 0 for security_deposit
airbnb <- airbnb %>%
mutate(security_deposit = if_else(is.na(security_deposit),0,security_deposit))
#Make NAs = 0 for cleaning_fee
airbnb <- airbnb %>%
mutate(cleaning_fee = if_else(is.na(cleaning_fee),0,cleaning_fee))
#Make NAs = 0 for review_scores_rating
airbnb <- airbnb %>%
mutate(review_scores_rating = case_when(
is.na(review_scores_rating) ~ 0,
!is.na(review_scores_rating) ~ review_scores_rating)
)
#Make NAs = 0 for review_scores_accuracy
airbnb <- airbnb %>%
mutate(review_scores_accuracy = case_when(
is.na(review_scores_accuracy) ~ 0,
!is.na(review_scores_accuracy) ~ review_scores_accuracy)
)
#Make NAs = 0 for review_scores_cleanliness
airbnb <- airbnb %>%
mutate(review_scores_cleanliness = case_when(
is.na(review_scores_cleanliness) ~ 0,
!is.na(review_scores_cleanliness) ~ review_scores_cleanliness)
)
#Make NAs = 0 for review_scores_checkin
airbnb <- airbnb %>%
mutate(review_scores_checkin = case_when(
is.na(review_scores_checkin) ~ 0,
!is.na(review_scores_checkin) ~ review_scores_checkin)
)
#Make NAs = 0 for review_scores_communcation
airbnb <- airbnb %>%
mutate(review_scores_communication = case_when(
is.na(review_scores_communication) ~ 0,
!is.na(review_scores_communication) ~ review_scores_communication)
)
#Make NAs = 0 for review_sores_location
airbnb <- airbnb %>%
mutate(review_scores_location = case_when(
is.na(review_scores_location) ~ 0,
!is.na(review_scores_location) ~ review_scores_location)
)
#Make NAs = 0 for review_scores_value
airbnb <- airbnb %>%
mutate(review_scores_value = case_when(
is.na(review_scores_value) ~ 0,
!is.na(review_scores_value) ~ review_scores_value)
)
#Make NAs = 0 for reviews_per_month
airbnb <- airbnb %>%
mutate(reviews_per_month = case_when(
is.na(reviews_per_month) ~ 0,
!is.na(reviews_per_month) ~ reviews_per_month)
)#Log transform reviews_per_month
airbnb <- airbnb %>%
mutate(reviews_per_month.1 = reviews_per_month + 1,
log.reviews_per_month = log(reviews_per_month.1))
#Log transform review_scores_rating
airbnb <- airbnb %>%
mutate(review_scores_rating.1 = review_scores_rating + 1,
log.review_scores_rating = log(review_scores_rating.1))
#Log transform reviews_scores_value
airbnb <- airbnb %>%
mutate(review_score_value.1 = review_scores_value + 1,
log.review_scores_value = log(review_score_value.1))
#Log transform review_scores_location
airbnb <- airbnb %>%
mutate(review_scores_location.1 = review_scores_location + 1,
log.review_scores_location = log(review_scores_location.1))
#Log transform review_scores_communication
airbnb <- airbnb %>%
mutate(review_scores_communication.1 = review_scores_communication + 1,
log.review_scores_communication = log(review_scores_communication.1))
#Log transform review_scores_checkin
airbnb <- airbnb %>%
mutate(review_scores_checkin.1 = review_scores_checkin + 1,
log.review_scores_checkin = log(review_scores_checkin.1))
#Log transform review_scores_accuracy
airbnb <- airbnb %>%
mutate(review_scores_accuracy.1 = review_scores_accuracy + 1,
log.review_scores_accuracy = log(review_scores_accuracy.1))
#Log transform review_scores_cleanliness
airbnb <- airbnb %>%
mutate(review_scores_cleanliness.1 = review_scores_cleanliness + 1,
log.review_scores_cleanliness = log(review_scores_cleanliness.1))
#Make NAs = 0 for host_response_rate
#airbnb <- airbnb %>%
#mutate(host_response_rate = case_when(
#is.na(host_response_rate) ~ 0.0,
#!is.na(host_response_rate) ~ host_response_rate)
#)#Make price as numeric
airbnb$price <- as.numeric(as.character(airbnb$price))## Warning: NAs introduced by coercionairbnb$price## [1] 55 765 225 77 75 220 107 71 26 125 134 58 65 60 68 60 100
## [18] 250 50 279 100 76 125 115 119 95 95 47 50 130 135 155 119 30
## [35] 75 49 45 49 250 309 175 99 224 137 65 95 62 200 115 145 130
## [52] 442 95 90 55 135 68 60 72 115 250 110 85 765 331 95 NA 57
## [69] 70 75 90 88 96 80 175 110 118 144 90 192 70 75 150 44 89
## [86] 80 275 55 60 99 87 79 89 216 60 28 109 150 48 88 99 89
## [103] 165 60 130 120 53 199 49 85 50 78 85 165 85 89 100 140 100
## [120] NA 375 79 195 205 65 79 668 190 77 135 100 97 160 105 110 135
## [137] 160 176 48 29 199 68 140 99 39 136 140 75 279 75 120 245 100
## [154] 59 65 70 97 51 96 119 110 90 125 75 135 275 37 125 245 120
## [171] 79 59 90 195 77 89 88 325 75 40 145 280 197 99 99 68 69
## [188] 240 199 70 65 65 125 99 60 70 75 88 129 59 80 52 86 75
## [205] 49 150 200 195 50 175 65 90 125 134 220 125 95 84 80 250 80
## [222] 101 127 275 130 180 115 65 250 49 89 70 95 98 155 700 75 310
## [239] 49 60 42 129 115 98 175 485 75 83 199 50 160 60 65 55 74
## [256] 90 150 86 49 50 125 219 110 40 80 66 75 100 99 105 250 65
## [273] 52 89 95 125 79 115 89 92 110 120 95 145 52 150 130 85 140
## [290] 53 115 27 72 47 89 115 350 78 107 55 89 79 99 56 125 115
## [307] 95 111 75 75 99 75 117 195 99 88 115 83 55 95 90 85 95
## [324] 50 149 59 39 240 85 95 80 60 90 125 52 105 250 85 50 220
## [341] 214 60 200 70 300 47 266 99 195 111 95 169 200 49 60 70 99
## [358] 85 70 130 57 149 100 65 200 89 190 145 39 250 110 120 195 87
## [375] 100 90 120 175 129 95 98 80 119 285 88 100 75 35 75 55 200
## [392] 75 110 70 84 89 240 28 70 39 80 115 140 40 85 75 100 290
## [409] 80 49 65 199 95 125 199 73 275 180 195 109 127 62 55 125 90
## [426] 125 219 135 90 230 99 60 69 195 75 89 65 119 79 95 175 90
## [443] 175 110 70 150 139 109 130 75 76 630 113 149 125 158 50 149 86
## [460] 92 99 40 170 95 100 64 249 125 109 150 105 80 125 99 44 124
## [477] 69 95 125 125 290 205 61 235 46 27 75 110 325 199 425 100 375
## [494] 85 125 147 175 80 49 89 49 67 225 125 40 110 100 60 66 148
## [511] 142 130 89 90 125 88 135 69 115 82 450 27 775 175 119 129 NA
## [528] 240 129 109 92 145 199 112 81 95 110 190 170 135 172 60 55 52
## [545] 80 125 300 150 55 55 59 75 145 80 150 155 69 91 85 60 130
## [562] 120 60 75 98 70 219 125 160 95 225 119 115 70 219 219 170 125
## [579] 59 75 144 61 55 59 51 350 150 30 165 150 80 55 127 85 40
## [596] 250 80 145 120 145 250 125 50 124 51 165 95 70 139 250 79 95
## [613] 50 85 121 110 40 100 75 79 165 70 95 199 63 67 129 90 40
## [630] 50 125 150 82 120 80 45 100 266 59 97 47 140 124 80 99 150
## [647] 150 100 48 125 80 150 56 80 49 249 48 160 130 99 56 450 141
## [664] 95 48 150 240 110 150 106 500 90 220 130 95 89 85 110 99 149
## [681] 90 150 125 105 120 90 77 131 70 185 60 125 62 89 85 67 74
## [698] 40 75 84 85 167 85 149 89 125 80 495 150 100 90 33 59 88
## [715] 110 50 120 243 89 90 145 295 90 50 250 115 45 95 54 75 160
## [732] 95 130 55 165 125 36 57 99 95 79 145 51 45 30 112 80 200
## [749] 40 79 65 275 80 225 135 60 230 149 45 71 285 500 76 125 60
## [766] 140 90 120 165 135 79 125 100 135 22 40 109 162 62 105 66 37
## [783] 172 99 100 88 195 50 128 220 210 98 149 445 90 99 100 100 129
## [800] 80 124 137 119 310 109 159 169 350 85 60 330 150 120 359 92 34
## [817] 175 50 69 250 200 150 275 225 46 900 450 450 450 335 335 275 775
## [834] 500 450 NA 149 35 89 55 125 78 40 70 99 129 75 115 62 375
## [851] 185 175 199 85 75 92 250 225 250 54 58 38 65 95 52 92 600
## [868] 350 225 99 200 120 74 80 87 110 124 99 85 55 120 119 62 60
## [885] 100 90 85 95 176 135 465 58 465 930 180 130 125 80 150 145 100
## [902] 225 45 111 249 60 90 90 125 90 80 75 100 86 105 199 89 79
## [919] 60 120 125 129 115 60 700 38 82 175 75 70 70 70 70 70 198
## [936] 80 90 45 90 72 128 92 70 65 85 70 70 70 90 145 95 62
## [953] 85 76 90 74 250 69 NA 65 95 80 90 69 119 75 79 73 60
## [970] 35 249 270 62 600 289 55 55 48 99 105 149 125 200 125 45 109
## [987] 84 79 60 79 79 250 110 105 525 78 125 85 91 65 167 80 150
## [1004] 175 82 300 150 375 70 42 69 65 70 330 110 95 125 160 200 110
## [1021] 285 188 175 90 285 59 65 95 195 170 89 38 120 99 184 225 125
## [1038] 100 84 75 125 179 80 165 259 75 75 115 64 95 135 99 70 65
## [1055] 52 65 47 120 62 120 49 355 50 51 58 185 125 150 72 55 89
## [1072] 93 65 149 59 70 200 65 165 375 75 60 75 285 125 95 225 85
## [1089] 80 85 95 200 40 45 125 119 149 61 70 110 85 150 110 85 81
## [1106] 160 99 50 250 65 245 125 95 289 68 105 135 30 330 102 70 96
## [1123] 70 90 75 144 63 195 135 98 42 150 200 85 250 310 60 159 49
## [1140] 68 50 125 89 925 129 115 138 93 175 105 195 100 39 320 70 40
## [1157] 325 335 85 185 69 90 10 95 169 199 99 60 99 75 295 75 125
## [1174] 325 107 62 250 70 45 78 125 68 57 145 99 130 39 109 80 115
## [1191] 20 135 80 125 250 100 150 120 99 85 145 135 65 50 77 57 155
## [1208] 70 85 140 110 79 70 85 49 300 150 87 130 100 75 700 88 97
## [1225] 87 175 100 150 115 120 80 150 51 51 80 60 375 49 125 125 80
## [1242] 125 60 140 99 49 25 165 89 305 89 63 39 69 100 69 60 149
## [1259] 265 350 43 305 75 65 100 95 80 185 33 98 125 119 135 135 79
## [1276] 90 100 43 115 100 96 225 115 75 50 375 125 500 195 90 140 100
## [1293] 100 110 75 225 50 125 75 150 99 125 225 150 55 99 105 79 195
## [1310] 57 225 95 40 40 180 63 110 65 199 50 195 200 99 63 185 211
## [1327] 110 55 150 50 119 99 125 175 210 39 150 65 90 61 100 111 100
## [1344] 150 190 72 68 70 140 120 250 179 127 95 32 30 199 69 90 97
## [1361] 90 45 45 130 69 100 60 120 120 100 125 120 40 160 175 95 65
## [1378] 129 80 544 375 190 175 165 35 320 35 295 135 77 71 55 75 114
## [1395] 119 60 180 50 40 101 91 80 134 68 90 125 40 75 38 125 395
## [1412] 150 60 60 105 75 110 400 63 70 106 250 115 60 229 120 65 100
## [1429] 195 127 150 55 80 175 90 90 50 80 120 500 43 70 85 62 85
## [1446] 52 24 299 80 68 120 37 115 139 84 157 89 225 125 73 99 266
## [1463] 90 99 385 75 59 68 80 60 150 195 199 135 55 275 150 200 125
## [1480] 145 210 85 225 NA 55 768 40 56 200 80 70 179 89 89 86 238
## [1497] 130 238 238 266 268 975 750 NA 155 40 75 65 90 195 165 74 223
## [1514] 101 46 79 75 11 106 95 125 115 168 199 95 275 92 175 75 250
## [1531] 95 99 65 100 105 82 58 110 75 240 109 50 75 150 69 80 120
## [1548] 119 250 99 250 100 99 85 99 100 62 480 75 69 75 106 49 129
## [1565] 215 100 75 85 70 145 110 40 17 68 100 195 50 100 120 275 80
## [1582] 100 89 99 90 65 62 89 185 150 95 100 155 285 100 40 65 71
## [1599] 105 585 119 225 41 70 24 50 399 125 250 17 75 200 129 180 115
## [1616] 240 60 250 425 85 50 177 200 19 150 110 99 149 65 178 80 88
## [1633] 60 79 99 75 85 144 60 250 250 75 225 55 35 99 NA 200 350
## [1650] 79 100 100 75 108 90 80 50 279 110 185 58 80 75 350 50 199
## [1667] 75 248 64 100 50 44 92 45 65 162 79 186 75 40 95 50 150
## [1684] 180 225 69 19 65 73 200 250 45 275 25 165 56 125 92 75 115
## [1701] 125 90 95 85 49 55 90 300 19 118 104 190 85 85 495 300 68
## [1718] 60 64 65 79 140 249 100 89 55 175 250 95 57 95 69 325 76
## [1735] 375 375 175 71 595 90 155 165 74 58 49 155 35 90 675 92 100
## [1752] 80 195 145 77 100 58 198 115 75 124 225 65 250 200 145 275 42
## [1769] 450 44 88 175 115 53 206 57 65 300 88 75 93 130 95 265 49
## [1786] 90 198 67 130 96 500 85 80 80 74 119 228 96 530 426 88 147
## [1803] 61 150 125 250 222 60 79 800 150 205 63 50 195 414 120 NA 377
## [1820] 509 175 85 150 59 50 75 469 399 89 80 205 375 611 255 255 100
## [1837] 425 NA 150 84 58 77 150 75 219 65 75 40 228 79 117 195 115
## [1854] 65 150 45 94 139 93 120 225 91 145 73 75 60 168 101 55 150
## [1871] 56 65 50 225 88 47 125 69 59 99 225 180 135 49 85 70 129
## [1888] 199 25 159 199 75 59 110 75 250 130 450 175 78 89 260 239 25
## [1905] 98 80 109 95 145 60 88 96 99 50 44 90 120 22 412 820 482
## [1922] 50 401 413 42 391 253 224 239 239 199 90 NA 60 110#Make host_response_rate as numeric
#airbnb$host_response_rate <- as.character(sub("%", "", airbnb$host_response_rate))
#airbnb$host_response_rate <- as.numeric(airbnb$host_response_rate)
#airbnb$host_response_rate#Make zipcode a factor
airbnb$zipcode <- as.factor(airbnb$zipcode)#Omit all observations with NAs
airbnb <- airbnb[complete.cases(airbnb),]Separate training and testing
#80% of the sample size
smp_size <- floor(0.80 * nrow(airbnb))
#set the seed to make your partition reproducible
set.seed(123456)
train_ind <- sample(seq_len(nrow(airbnb)), size = smp_size)
train.airbnb <- airbnb[train_ind, ]
test.airbnb <- airbnb[-train_ind, ]train.airbnb <- train.airbnb %>% mutate(log.bathrooms = log(bathrooms),
log.securitydeposit = log(security_deposit),
log.guestsincluded = log(guests_included),
log.nreviews = log(number_of_reviews))Description of data
Question of interest: How can we produce a model that accurately predicts the listed nightly price for an Airbnb in Asheville, NC?
The data set we are using is a .csv file of every AirBnB listing in the city of Asheville, North Carolina as of October 17, 2018 . Each observation is an individual listing. We sourced this data from Inside AirBnB, a website that regularly scrapes data from AirBnB’s listings and provides them as public data sets separated by city.
The original data set was very large (96 columns and 1,936 observations), so we reduced it for simplicity’s sake. We chose 26 columns that could potentially be of interest for a regression analysis, and we created one more column called has_reviews, which is an indicator variable. We noticed that some columns, like cleaning_fee and security_deposit, had a lot of NAs, so instead of omitting all of these observations we mutated NAs from these columns to be 0s. We were left with 24 incomplete cases, likely the result of web scraping errors, and so we chose to omit them. Our final number of columns was 27 and our final number of rows was 1,911.
Variables: * host_response_rate * host_is_superhost * host_listings_count * zipcode * property_type * room_type * accomodates * bathrooms * beds * bed_type * price * security_deposit * cleaning_fee * guests_included * extra_people_cost * minimum_nights * maximum_nights * availability_30 * number_of_reviews * review_scores_rating * review_scores_accuracy * review_scores_cleanliness * review_scores_checkin * review_scores_communication * review_scores_location * review_scores_value * reviews_per_month * cancellation_policy
Background
Airbnb, inc. is a privately held global company headquartered in San Francisco that operates as a broker for lodging arrangements. Made famous by celebrities like Kim Kardashian, the company is revolutionizing the way people vacation. Rather than booking a hotel, users can go on the AirBnB website or mobile app and quickly rent private rooms, guest suites or even entire homes to themselves. The company has often faced controversy surrounding housing affordability, pricing transparency, privacy and hotel industry competition. Despite these concerns, it blew by its own internal forecasts and brought in 2.6 billion dollars in revenue and 93 million in profit by the end of 2017. For a company that exclusively makes money by taking a small commission (3%) of the price of every listing, that’s pretty impressive.
We were interested in this data because it’s something that so many people, especially our peers here at Duke, would find relevant. There are over 4 million AirBnB listings worldwide and 150 million global users. Both Mary Helen and I have stayed in an AirBnB in the last month. With the option to rent entire homes, AirBnBs offer more luxury, space and solitude than other lodging options. Hosts set prices for listings at their own discretion, and so there isn’t any specific algorithm or model by which it’s calculated. By using this data to create a model that can accurately predict prices for listings, we might be able to help people figure out what the typical price range is for the type of listing they want – and therefore, whether or not a specific listing is a good deal. Specifically, we’ll be looking at AirBnB listings in the Asheville Metro Area, North Carolina. Asheville is a popular weekend getaway in North Carolina. Given its relative proximity to Duke, many students visit at least once during their time here – often staying in AirBnBs when they do. This makes our data more relevant to our peers, and also helps us by narrowing down the total number of observations into a size that’s more manageable.
Exploratory Data Analysis
#Pairs plots for all of the explanatory variables
pairs(price ~ host_response_rate + host_is_superhost + host_listings_count, data=train.airbnb)
pairs(price ~ zipcode + room_type + bathrooms, data=train.airbnb)
pairs(price ~ accommodates + beds + bed_type, data=train.airbnb)
pairs(price ~ security_deposit + cleaning_fee + guests_included, data = train.airbnb)
pairs(price ~ extra_people + minimum_nights + availability_30, data = train.airbnb)
pairs(price ~ number_of_reviews + review_scores_rating + review_scores_accuracy, data = train.airbnb)
pairs(price ~ review_scores_cleanliness + review_scores_checkin + review_scores_communication, data = train.airbnb)
pairs(price ~ review_scores_location + review_scores_value + reviews_per_month, data = train.airbnb)
pairs(price ~ cancellation_policy, data = train.airbnb)
#Pairs with log.bathrooms, log.cleaningfee, log.securitydeposit, log.guestsincluded, log.nreviews
pairs(price ~ log.securitydeposit + log.guestsincluded + log.nreviews, data = train.airbnb)
#Distribution of nightly price
ggplot(train.airbnb, aes(x=price)) + geom_histogram(stat="count")
#Boxplot of price by bed type
ggplot(train.airbnb, aes(x=bed_type, y=price)) + geom_boxplot()
pairs(price ~ zipcode + room_type + bathrooms, data=train.airbnb)
pairs(price ~ accommodates + beds + bed_type, data=train.airbnb)
pairs(price ~ security_deposit + cleaning_fee + guests_included, data = train.airbnb)
pairs(price ~ extra_people + minimum_nights + availability_30, data = train.airbnb)
pairs(price ~ number_of_reviews + review_scores_rating + review_scores_accuracy, data = train.airbnb)
pairs(price ~ review_scores_cleanliness + review_scores_checkin + review_scores_communication, data = train.airbnb)
pairs(price ~ review_scores_location + review_scores_value + reviews_per_month, data = train.airbnb)
pairs(price ~ cancellation_policy, data = train.airbnb)
#Pairs with log.bathrooms, log.cleaningfee, log.securitydeposit, log.guestsincluded, log.nreviews
pairs(price ~ log.bathrooms + log.cleaningfee, data = train.airbnb)
pairs(price ~ log.securitydeposit + log.guestsincluded + log.nreviews, data = train.airbnb)
#Distribution of nightly price
ggplot(train.airbnb, aes(x=price)) + geom_histogram(stat="count")
#Boxplot of price by bed type
ggplot(train.airbnb, aes(x=bed_type, y=price)) + geom_boxplot()
Model building
NOTE -> we are omitting host_response_rate from our model because we were having trouble converting the variable to a numeric without losing a lot of the information. Will address before final due date.
full.model <- lm(price ~ host_is_superhost
+ host_listings_count
+ zipcode
+ room_type
+ accommodates
+ bathrooms
+ beds
+ bed_type
+ cleaning_fee
+ extra_people
+ minimum_nights
+ availability_30
+ number_of_reviews
+ log.review_scores_rating
+ log.review_scores_accuracy
+ log.review_scores_cleanliness
+ log.review_scores_checkin
+ log.review_scores_communication
+ log.review_scores_location
+ log.review_scores_value
+ log.reviews_per_month
+ cancellation_policy, data=train.airbnb)
kable(tidy(full.model), digits=3)| term | estimate | std.error | statistic | p.value |
|---|---|---|---|---|
| (Intercept) | -6.939 | 36.364 | -0.191 | 0.849 |
| host_is_superhostt | 6.008 | 3.731 | 1.610 | 0.108 |
| host_listings_count | 0.013 | 0.084 | 0.150 | 0.881 |
| zipcode28715 | -17.992 | 13.749 | -1.309 | 0.191 |
| zipcode28732 | 4.433 | 14.591 | 0.304 | 0.761 |
| zipcode28748 | -22.233 | 61.031 | -0.364 | 0.716 |
| zipcode28787 | 39.474 | 61.165 | 0.645 | 0.519 |
| zipcode28801 | 42.285 | 8.269 | 5.114 | 0.000 |
| zipcode28803 | 22.266 | 8.419 | 2.645 | 0.008 |
| zipcode28804 | 29.145 | 8.632 | 3.377 | 0.001 |
| zipcode28805 | 16.540 | 8.657 | 1.911 | 0.056 |
| zipcode28806 | 4.091 | 7.865 | 0.520 | 0.603 |
| zipcode28815 | 23.355 | 61.197 | 0.382 | 0.703 |
| zipcode29710 | -8.802 | 61.156 | -0.144 | 0.886 |
| room_typePrivate room | -20.297 | 4.010 | -5.062 | 0.000 |
| room_typeShared room | -79.926 | 23.747 | -3.366 | 0.001 |
| accommodates | 13.099 | 1.622 | 8.076 | 0.000 |
| bathrooms | 43.293 | 3.816 | 11.347 | 0.000 |
| beds | -0.624 | 2.453 | -0.254 | 0.799 |
| bed_typeCouch | 13.174 | 69.925 | 0.188 | 0.851 |
| bed_typeFuton | 31.961 | 41.827 | 0.764 | 0.445 |
| bed_typePull-out Sofa | 42.474 | 49.705 | 0.855 | 0.393 |
| bed_typeReal Bed | 32.667 | 35.033 | 0.932 | 0.351 |
| cleaning_fee | 0.308 | 0.048 | 6.420 | 0.000 |
| extra_people | 0.009 | 0.076 | 0.118 | 0.906 |
| minimum_nights | -2.077 | 0.212 | -9.792 | 0.000 |
| availability_30 | 0.560 | 0.202 | 2.773 | 0.006 |
| number_of_reviews | 0.014 | 0.026 | 0.544 | 0.586 |
| log.review_scores_rating | -24.040 | 12.841 | -1.872 | 0.061 |
| log.review_scores_accuracy | -52.903 | 57.657 | -0.918 | 0.359 |
| log.review_scores_cleanliness | 135.420 | 35.304 | 3.836 | 0.000 |
| log.review_scores_checkin | -62.905 | 60.622 | -1.038 | 0.300 |
| log.review_scores_communication | -11.178 | 46.949 | -0.238 | 0.812 |
| log.review_scores_location | 77.630 | 42.880 | 1.810 | 0.070 |
| log.review_scores_value | -43.160 | 39.570 | -1.091 | 0.276 |
| log.reviews_per_month | -26.636 | 3.650 | -7.297 | 0.000 |
| cancellation_policymoderate | 2.856 | 4.329 | 0.660 | 0.510 |
| cancellation_policystrict_14_with_grace_period | 11.439 | 4.766 | 2.400 | 0.017 |
| cancellation_policysuper_strict_30 | 6.954 | 15.502 | 0.449 | 0.654 |
| cancellation_policysuper_strict_60 | 206.731 | 14.862 | 13.910 | 0.000 |
backward.model <- ols_step_backward_aic(full.model, details=TRUE)## Backward Elimination Method
## ---------------------------
##
## Candidate Terms:
##
## 1 . host_is_superhost
## 2 . host_listings_count
## 3 . zipcode
## 4 . room_type
## 5 . accommodates
## 6 . bathrooms
## 7 . beds
## 8 . bed_type
## 9 . cleaning_fee
## 10 . extra_people
## 11 . minimum_nights
## 12 . availability_30
## 13 . number_of_reviews
## 14 . log.review_scores_rating
## 15 . log.review_scores_accuracy
## 16 . log.review_scores_cleanliness
## 17 . log.review_scores_checkin
## 18 . log.review_scores_communication
## 19 . log.review_scores_location
## 20 . log.review_scores_value
## 21 . log.reviews_per_month
## 22 . cancellation_policy
##
## Step 0: AIC = 16814.84
## price ~ host_is_superhost + host_listings_count + zipcode + room_type + accommodates + bathrooms + beds + bed_type + cleaning_fee + extra_people + minimum_nights + availability_30 + number_of_reviews + log.review_scores_rating + log.review_scores_accuracy + log.review_scores_cleanliness + log.review_scores_checkin + log.review_scores_communication + log.review_scores_location + log.review_scores_value + log.reviews_per_month + cancellation_policy
##
## -----------------------------------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## -----------------------------------------------------------------------------------------------------
## extra_people 1 16812.857 50.894 5373806.868 0.688 0.680
## host_listings_count 1 16812.866 81.238 5373837.212 0.688 0.680
## log.review_scores_communication 1 16812.901 205.832 5373961.807 0.688 0.680
## beds 1 16812.909 235.055 5373991.029 0.688 0.680
## number_of_reviews 1 16813.147 1075.499 5374831.473 0.688 0.680
## log.review_scores_accuracy 1 16813.707 3056.829 5376812.803 0.688 0.680
## bed_type 1 16807.920 3809.540 5377565.514 0.688 0.680
## log.review_scores_checkin 1 16813.948 3909.543 5377665.518 0.688 0.680
## log.review_scores_value 1 16814.064 4319.592 5378075.566 0.688 0.680
## host_is_superhost 1 16815.504 9415.425 5383171.399 0.687 0.679
## log.review_scores_location 1 16816.205 11900.343 5385656.317 0.687 0.679
## log.review_scores_rating 1 16816.438 12726.193 5386482.167 0.687 0.679
## availability_30 1 16820.718 27914.132 5401670.107 0.686 0.678
## log.review_scores_cleanliness 1 16827.879 53423.437 5427179.411 0.685 0.677
## room_type 1 16844.527 120414.474 5494170.448 0.681 0.673
## cleaning_fee 1 16854.595 149655.892 5523411.866 0.679 0.671
## log.reviews_per_month 1 16866.566 193329.879 5567085.853 0.677 0.668
## accommodates 1 16878.389 236800.138 5610556.112 0.674 0.666
## zipcode 1 16887.019 343479.206 5717235.180 0.668 0.662
## minimum_nights 1 16908.260 348148.667 5721904.641 0.668 0.659
## bathrooms 1 16939.630 467464.381 5841220.355 0.661 0.652
## cancellation_policy 1 17003.873 743737.822 6117493.796 0.645 0.636
## -----------------------------------------------------------------------------------------------------
##
##
## - bed_type
##
##
## Step 1 : AIC = 16807.92
## price ~ host_is_superhost + host_listings_count + zipcode + room_type + accommodates + bathrooms + beds + cleaning_fee + extra_people + minimum_nights + availability_30 + number_of_reviews + log.review_scores_rating + log.review_scores_accuracy + log.review_scores_cleanliness + log.review_scores_checkin + log.review_scores_communication + log.review_scores_location + log.review_scores_value + log.reviews_per_month + cancellation_policy
##
## -----------------------------------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## -----------------------------------------------------------------------------------------------------
## extra_people 1 16805.935 54.003 5377619.517 0.688 0.681
## host_listings_count 1 16805.944 84.086 5377649.600 0.688 0.681
## log.review_scores_communication 1 16805.975 195.597 5377761.111 0.688 0.681
## beds 1 16805.991 251.115 5377816.629 0.688 0.681
## number_of_reviews 1 16806.218 1054.437 5378619.951 0.688 0.681
## log.review_scores_accuracy 1 16806.815 3169.473 5380734.987 0.688 0.680
## log.review_scores_checkin 1 16807.017 3882.429 5381447.943 0.688 0.680
## log.review_scores_value 1 16807.115 4231.616 5381797.131 0.688 0.680
## host_is_superhost 1 16808.586 9442.094 5387007.608 0.687 0.680
## log.review_scores_location 1 16809.288 11928.347 5389493.861 0.687 0.680
## log.review_scores_rating 1 16809.487 12635.290 5390200.804 0.687 0.680
## availability_30 1 16813.992 28635.427 5406200.941 0.686 0.679
## log.review_scores_cleanliness 1 16820.928 53358.800 5430924.314 0.685 0.677
## room_type 1 16838.107 122318.895 5499884.409 0.681 0.674
## cleaning_fee 1 16847.667 149741.472 5527306.986 0.679 0.672
## log.reviews_per_month 1 16860.009 194806.406 5572371.920 0.676 0.669
## accommodates 1 16871.855 238403.004 5615968.518 0.674 0.666
## zipcode 1 16879.536 341612.375 5719177.889 0.668 0.663
## minimum_nights 1 16900.908 346778.760 5724344.274 0.668 0.660
## bathrooms 1 16932.517 467064.989 5844630.503 0.661 0.653
## cancellation_policy 1 16996.975 744365.082 6121930.596 0.645 0.637
## -----------------------------------------------------------------------------------------------------
##
## - extra_people
##
##
## Step 2 : AIC = 16805.94
## price ~ host_is_superhost + host_listings_count + zipcode + room_type + accommodates + bathrooms + beds + cleaning_fee + minimum_nights + availability_30 + number_of_reviews + log.review_scores_rating + log.review_scores_accuracy + log.review_scores_cleanliness + log.review_scores_checkin + log.review_scores_communication + log.review_scores_location + log.review_scores_value + log.reviews_per_month + cancellation_policy
##
## -----------------------------------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## -----------------------------------------------------------------------------------------------------
## host_listings_count 1 16803.956 74.697 5377694.214 0.688 0.681
## log.review_scores_communication 1 16803.990 194.984 5377814.502 0.688 0.681
## beds 1 16804.008 259.217 5377878.734 0.688 0.681
## number_of_reviews 1 16804.237 1066.749 5378686.266 0.688 0.681
## log.review_scores_accuracy 1 16804.823 3143.560 5380763.078 0.688 0.681
## log.review_scores_checkin 1 16805.037 3900.723 5381520.240 0.688 0.681
## log.review_scores_value 1 16805.142 4271.024 5381890.541 0.688 0.681
## host_is_superhost 1 16806.631 9547.447 5387166.965 0.687 0.680
## log.review_scores_location 1 16807.313 11962.843 5389582.360 0.687 0.680
## log.review_scores_rating 1 16807.504 12642.745 5390262.262 0.687 0.680
## availability_30 1 16812.071 28859.823 5406479.341 0.686 0.679
## log.review_scores_cleanliness 1 16818.936 53335.780 5430955.297 0.685 0.678
## room_type 1 16836.142 122392.325 5500011.842 0.681 0.674
## cleaning_fee 1 16846.048 151074.151 5528693.668 0.679 0.672
## log.reviews_per_month 1 16858.177 195368.303 5572987.820 0.676 0.669
## accommodates 1 16870.376 240275.271 5617894.789 0.674 0.667
## zipcode 1 16877.638 341943.525 5719563.043 0.668 0.663
## minimum_nights 1 16899.040 347220.366 5724839.883 0.668 0.660
## bathrooms 1 16930.946 468659.215 5846278.732 0.661 0.653
## cancellation_policy 1 16995.055 744632.148 6122251.665 0.645 0.637
## -----------------------------------------------------------------------------------------------------
##
## - host_listings_count
##
##
## Step 3 : AIC = 16803.96
## price ~ host_is_superhost + zipcode + room_type + accommodates + bathrooms + beds + cleaning_fee + minimum_nights + availability_30 + number_of_reviews + log.review_scores_rating + log.review_scores_accuracy + log.review_scores_cleanliness + log.review_scores_checkin + log.review_scores_communication + log.review_scores_location + log.review_scores_value + log.reviews_per_month + cancellation_policy
##
## -----------------------------------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## -----------------------------------------------------------------------------------------------------
## log.review_scores_communication 1 16802.019 222.956 5377917.170 0.688 0.681
## beds 1 16802.045 313.723 5378007.938 0.688 0.681
## number_of_reviews 1 16802.259 1071.375 5378765.590 0.688 0.681
## log.review_scores_accuracy 1 16802.848 3156.239 5380850.454 0.688 0.681
## log.review_scores_checkin 1 16803.047 3861.586 5381555.801 0.688 0.681
## log.review_scores_value 1 16803.152 4230.816 5381925.030 0.688 0.681
## host_is_superhost 1 16804.633 9478.394 5387172.608 0.687 0.681
## log.review_scores_location 1 16805.357 12044.103 5389738.318 0.687 0.680
## log.review_scores_rating 1 16805.544 12708.748 5390402.963 0.687 0.680
## availability_30 1 16810.100 28888.894 5406583.108 0.686 0.679
## log.review_scores_cleanliness 1 16816.952 53316.651 5431010.865 0.685 0.678
## room_type 1 16834.153 122356.977 5500051.191 0.681 0.674
## cleaning_fee 1 16848.722 168026.607 5545720.822 0.678 0.671
## log.reviews_per_month 1 16856.177 195294.148 5572988.363 0.676 0.669
## accommodates 1 16868.854 241968.759 5619662.973 0.674 0.667
## zipcode 1 16875.739 342248.019 5719942.234 0.668 0.663
## minimum_nights 1 16897.548 349061.030 5726755.245 0.668 0.660
## bathrooms 1 16929.023 468884.147 5846578.362 0.661 0.653
## cancellation_policy 1 17045.324 958746.108 6336440.323 0.632 0.625
## -----------------------------------------------------------------------------------------------------
##
## - log.review_scores_communication
##
##
## Step 4 : AIC = 16802.02
## price ~ host_is_superhost + zipcode + room_type + accommodates + bathrooms + beds + cleaning_fee + minimum_nights + availability_30 + number_of_reviews + log.review_scores_rating + log.review_scores_accuracy + log.review_scores_cleanliness + log.review_scores_checkin + log.review_scores_location + log.review_scores_value + log.reviews_per_month + cancellation_policy
##
## ---------------------------------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## ---------------------------------------------------------------------------------------------------
## beds 1 16800.107 311.007 5378228.177 0.688 0.681
## number_of_reviews 1 16800.321 1067.909 5378985.080 0.688 0.681
## log.review_scores_accuracy 1 16801.048 3640.160 5381557.330 0.688 0.681
## log.review_scores_value 1 16801.345 4693.817 5382610.988 0.687 0.681
## log.review_scores_checkin 1 16801.864 6530.653 5384447.824 0.687 0.681
## host_is_superhost 1 16802.682 9427.801 5387344.971 0.687 0.681
## log.review_scores_location 1 16803.486 12280.357 5390197.527 0.687 0.681
## log.review_scores_rating 1 16803.687 12991.612 5390908.783 0.687 0.680
## availability_30 1 16808.166 28901.526 5406818.696 0.686 0.680
## log.review_scores_cleanliness 1 16815.086 53573.323 5431490.493 0.685 0.678
## room_type 1 16832.175 122212.902 5500130.072 0.681 0.674
## cleaning_fee 1 16846.821 168164.249 5546081.419 0.678 0.671
## log.reviews_per_month 1 16854.257 195365.070 5573282.241 0.676 0.670
## accommodates 1 16866.985 242229.405 5620146.576 0.674 0.667
## zipcode 1 16873.791 342222.421 5720139.591 0.668 0.663
## minimum_nights 1 16895.701 349412.837 5727330.008 0.667 0.661
## bathrooms 1 16927.028 468679.816 5846596.986 0.661 0.653
## cancellation_policy 1 17043.331 958552.392 6336469.563 0.632 0.625
## ---------------------------------------------------------------------------------------------------
##
## - beds
##
##
## Step 5 : AIC = 16800.11
## price ~ host_is_superhost + zipcode + room_type + accommodates + bathrooms + cleaning_fee + minimum_nights + availability_30 + number_of_reviews + log.review_scores_rating + log.review_scores_accuracy + log.review_scores_cleanliness + log.review_scores_checkin + log.review_scores_location + log.review_scores_value + log.reviews_per_month + cancellation_policy
##
## ---------------------------------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## ---------------------------------------------------------------------------------------------------
## number_of_reviews 1 16798.420 1108.099 5379336.276 0.688 0.681
## log.review_scores_accuracy 1 16799.149 3686.993 5381915.170 0.688 0.681
## log.review_scores_value 1 16799.432 4688.650 5382916.828 0.687 0.681
## log.review_scores_checkin 1 16799.953 6535.797 5384763.975 0.687 0.681
## host_is_superhost 1 16800.747 9348.008 5387576.185 0.687 0.681
## log.review_scores_location 1 16801.590 12337.853 5390566.030 0.687 0.681
## log.review_scores_rating 1 16801.799 13077.906 5391306.083 0.687 0.681
## availability_30 1 16806.313 29114.348 5407342.525 0.686 0.680
## log.review_scores_cleanliness 1 16813.249 53842.822 5432070.999 0.685 0.678
## room_type 1 16830.565 123316.316 5501544.493 0.681 0.674
## cleaning_fee 1 16844.821 167854.107 5546082.285 0.678 0.672
## log.reviews_per_month 1 16852.364 195445.061 5573673.239 0.676 0.670
## zipcode 1 16871.794 341922.035 5720150.213 0.668 0.663
## minimum_nights 1 16894.910 353660.437 5731888.614 0.667 0.661
## bathrooms 1 16925.543 470347.071 5848575.248 0.660 0.654
## accommodates 1 16947.272 554556.763 5932784.940 0.656 0.649
## cancellation_policy 1 17049.107 990742.327 6368970.504 0.630 0.624
## ---------------------------------------------------------------------------------------------------
##
## - number_of_reviews
##
##
## Step 6 : AIC = 16798.42
## price ~ host_is_superhost + zipcode + room_type + accommodates + bathrooms + cleaning_fee + minimum_nights + availability_30 + log.review_scores_rating + log.review_scores_accuracy + log.review_scores_cleanliness + log.review_scores_checkin + log.review_scores_location + log.review_scores_value + log.reviews_per_month + cancellation_policy
##
## ---------------------------------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## ---------------------------------------------------------------------------------------------------
## log.review_scores_accuracy 1 16797.435 3591.190 5382927.466 0.687 0.681
## log.review_scores_value 1 16797.735 4653.639 5383989.916 0.687 0.681
## log.review_scores_checkin 1 16798.202 6309.407 5385645.684 0.687 0.681
## host_is_superhost 1 16799.218 9911.426 5389247.703 0.687 0.681
## log.review_scores_location 1 16799.817 12035.128 5391371.404 0.687 0.681
## log.review_scores_rating 1 16800.204 13406.145 5392742.421 0.687 0.681
## availability_30 1 16804.510 28705.983 5408042.259 0.686 0.680
## log.review_scores_cleanliness 1 16811.402 53282.299 5432618.575 0.685 0.678
## room_type 1 16828.609 122364.571 5501700.848 0.681 0.675
## cleaning_fee 1 16842.835 166797.708 5546133.984 0.678 0.672
## log.reviews_per_month 1 16862.826 240220.796 5619557.072 0.674 0.667
## zipcode 1 16871.286 346431.217 5725767.493 0.668 0.663
## minimum_nights 1 16892.911 352555.610 5731891.886 0.667 0.661
## bathrooms 1 16924.090 471346.001 5850682.278 0.660 0.654
## accommodates 1 16945.444 554120.123 5933456.399 0.656 0.649
## cancellation_policy 1 17048.143 993974.717 6373310.993 0.630 0.624
## ---------------------------------------------------------------------------------------------------
##
## - log.review_scores_accuracy
##
##
## Step 7 : AIC = 16797.43
## price ~ host_is_superhost + zipcode + room_type + accommodates + bathrooms + cleaning_fee + minimum_nights + availability_30 + log.review_scores_rating + log.review_scores_cleanliness + log.review_scores_checkin + log.review_scores_location + log.review_scores_value + log.reviews_per_month + cancellation_policy
##
## ----------------------------------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## ----------------------------------------------------------------------------------------------------
## log.review_scores_value 1 16797.123 5984.112 5388911.579 0.687 0.681
## log.review_scores_location 1 16797.966 8972.390 5391899.856 0.687 0.681
## host_is_superhost 1 16798.304 10170.641 5393098.107 0.687 0.681
## log.review_scores_checkin 1 16798.921 12360.584 5395288.050 0.687 0.681
## log.review_scores_rating 1 16799.798 15474.638 5398402.104 0.687 0.681
## availability_30 1 16803.729 29453.181 5412380.647 0.686 0.680
## log.review_scores_cleanliness 1 16809.592 50371.415 5433298.881 0.685 0.679
## room_type 1 16827.162 120776.634 5503704.100 0.680 0.675
## cleaning_fee 1 16841.913 167139.868 5550067.334 0.678 0.672
## log.reviews_per_month 1 16861.602 239499.685 5622427.151 0.674 0.667
## zipcode 1 16871.125 349772.145 5732699.612 0.667 0.663
## minimum_nights 1 16891.281 350361.243 5733288.709 0.667 0.661
## bathrooms 1 16923.035 471391.906 5854319.372 0.660 0.654
## accommodates 1 16944.475 554553.790 5937481.256 0.655 0.649
## cancellation_policy 1 17048.580 1000611.645 6383539.112 0.629 0.623
## ----------------------------------------------------------------------------------------------------
##
## - log.review_scores_value
##
##
## Step 8 : AIC = 16797.12
## price ~ host_is_superhost + zipcode + room_type + accommodates + bathrooms + cleaning_fee + minimum_nights + availability_30 + log.review_scores_rating + log.review_scores_cleanliness + log.review_scores_checkin + log.review_scores_location + log.reviews_per_month + cancellation_policy
##
## ----------------------------------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## ----------------------------------------------------------------------------------------------------
## log.review_scores_location 1 16797.122 7088.365 5395999.944 0.687 0.681
## host_is_superhost 1 16797.572 8687.262 5397598.840 0.687 0.681
## log.review_scores_rating 1 16800.062 17538.571 5406450.149 0.686 0.680
## log.review_scores_checkin 1 16801.145 21390.456 5410302.035 0.686 0.680
## availability_30 1 16803.920 31277.536 5420189.115 0.685 0.680
## log.review_scores_cleanliness 1 16807.666 44651.603 5433563.181 0.685 0.679
## room_type 1 16827.657 123835.545 5512747.123 0.680 0.674
## cleaning_fee 1 16842.515 170664.520 5559576.098 0.677 0.671
## log.reviews_per_month 1 16864.366 251164.729 5640076.307 0.673 0.667
## minimum_nights 1 16892.104 355034.047 5743945.626 0.667 0.660
## zipcode 1 16874.468 363974.745 5752886.324 0.666 0.662
## bathrooms 1 16921.234 466176.319 5855087.897 0.660 0.654
## accommodates 1 16945.646 560972.180 5949883.758 0.655 0.648
## cancellation_policy 1 17054.641 1028570.936 6417482.515 0.627 0.621
## ----------------------------------------------------------------------------------------------------
##
## - log.review_scores_location
##
##
## Step 9 : AIC = 16797.12
## price ~ host_is_superhost + zipcode + room_type + accommodates + bathrooms + cleaning_fee + minimum_nights + availability_30 + log.review_scores_rating + log.review_scores_cleanliness + log.review_scores_checkin + log.reviews_per_month + cancellation_policy
##
## ----------------------------------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## ----------------------------------------------------------------------------------------------------
## host_is_superhost 1 16797.779 9443.038 5405442.981 0.686 0.681
## log.review_scores_checkin 1 16799.278 14775.991 5410775.934 0.686 0.680
## log.review_scores_rating 1 16799.326 14945.111 5410945.054 0.686 0.680
## availability_30 1 16803.838 31032.394 5427032.338 0.685 0.679
## log.review_scores_cleanliness 1 16809.836 52489.721 5448489.665 0.684 0.678
## room_type 1 16827.994 125227.301 5521227.245 0.679 0.674
## cleaning_fee 1 16842.254 169943.293 5565943.237 0.677 0.671
## log.reviews_per_month 1 16863.884 249712.375 5645712.318 0.672 0.667
## minimum_nights 1 16892.868 358398.760 5754398.704 0.666 0.660
## zipcode 1 16878.423 379470.035 5775469.979 0.665 0.661
## bathrooms 1 16923.059 473838.546 5869838.490 0.659 0.653
## accommodates 1 16944.196 556033.695 5952033.638 0.654 0.648
## cancellation_policy 1 17054.556 1029573.215 6425573.159 0.627 0.621
## ----------------------------------------------------------------------------------------------------
##
##
## No more variables to be removed.
##
## Variables Removed:
##
## - bed_type
## - extra_people
## - host_listings_count
## - log.review_scores_communication
## - beds
## - number_of_reviews
## - log.review_scores_accuracy
## - log.review_scores_value
## - log.review_scores_location
##
##
## Final Model Output
## ------------------
##
## Model Summary
## ----------------------------------------------------------------
## R 0.829 RMSE 60.138
## R-Squared 0.687 Coef. Var 45.750
## Adj. R-Squared 0.681 MSE 3616.622
## Pred R-Squared -Inf MAE 39.571
## ----------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## ---------------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## ---------------------------------------------------------------------------
## Regression 11828344.256 27 438086.824 121.131 0.0000
## Residual 5395999.944 1492 3616.622
## Total 17224344.200 1519
## ---------------------------------------------------------------------------
##
## Parameter Estimates
## -------------------------------------------------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## -------------------------------------------------------------------------------------------------------------------------------
## (Intercept) 24.267 10.544 2.301 0.022 3.584 44.951
## host_is_superhostt 5.920 3.664 0.027 1.616 0.106 -1.266 13.106
## zipcode28715 -17.741 13.685 -0.022 -1.296 0.195 -44.585 9.103
## zipcode28732 4.558 14.475 0.005 0.315 0.753 -23.836 32.952
## zipcode28748 -22.662 60.710 -0.005 -0.373 0.709 -141.748 96.424
## zipcode28787 45.098 60.955 0.011 0.740 0.460 -74.468 164.664
## zipcode28801 44.603 8.105 0.176 5.503 0.000 28.705 60.502
## zipcode28803 23.491 8.359 0.077 2.810 0.005 7.094 39.888
## zipcode28804 30.290 8.554 0.092 3.541 0.000 13.511 47.069
## zipcode28805 18.051 8.580 0.055 2.104 0.036 1.221 34.881
## zipcode28806 5.136 7.783 0.022 0.660 0.509 -10.131 20.402
## zipcode28815 26.024 60.782 0.006 0.428 0.669 -93.203 145.252
## zipcode29710 -7.412 60.952 -0.002 -0.122 0.903 -126.973 112.148
## room_typePrivate room -20.375 3.954 -0.087 -5.154 0.000 -28.130 -12.620
## room_typeShared room -81.857 23.571 -0.052 -3.473 0.001 -128.093 -35.620
## accommodates 12.792 1.032 0.284 12.399 0.000 10.768 14.815
## bathrooms 43.035 3.760 0.256 11.446 0.000 35.660 50.410
## cleaning_fee 0.311 0.045 0.158 6.855 0.000 0.222 0.400
## minimum_nights -2.086 0.210 -0.162 -9.955 0.000 -2.496 -1.675
## availability_30 0.586 0.200 0.044 2.929 0.003 0.194 0.978
## log.review_scores_rating -25.395 12.493 -0.305 -2.033 0.042 -49.900 -0.890
## log.review_scores_cleanliness 111.975 29.393 0.703 3.810 0.000 54.320 169.630
## log.review_scores_checkin -66.567 32.933 -0.419 -2.021 0.043 -131.167 -1.967
## log.reviews_per_month -26.050 3.135 -0.166 -8.309 0.000 -32.199 -19.900
## cancellation_policymoderate 3.225 4.245 0.015 0.760 0.448 -5.103 11.552
## cancellation_policystrict_14_with_grace_period 12.178 4.630 0.053 2.630 0.009 3.097 21.260
## cancellation_policysuper_strict_30 5.536 15.351 0.006 0.361 0.718 -24.576 35.648
## cancellation_policysuper_strict_60 210.840 12.915 0.271 16.325 0.000 185.506 236.174
## -------------------------------------------------------------------------------------------------------------------------------final.main.model <- lm(price ~ host_is_superhost
+ zipcode
+ room_type
+ accommodates
+ bathrooms
+ cleaning_fee
+ minimum_nights
+ availability_30
+ review_scores_cleanliness
+ review_scores_checkin
+ review_scores_location
+ review_scores_value
+ reviews_per_month
+ cancellation_policy, data=train.airbnb)
kable(tidy(final.main.model), digits=3)| term | estimate | std.error | statistic | p.value |
|---|---|---|---|---|
| (Intercept) | 23.755 | 10.637 | 2.233 | 0.026 |
| host_is_superhostt | 2.753 | 3.677 | 0.749 | 0.454 |
| zipcode28715 | -19.840 | 13.805 | -1.437 | 0.151 |
| zipcode28732 | 2.895 | 14.594 | 0.198 | 0.843 |
| zipcode28748 | -28.538 | 61.201 | -0.466 | 0.641 |
| zipcode28787 | 40.901 | 61.578 | 0.664 | 0.507 |
| zipcode28801 | 39.916 | 8.264 | 4.830 | 0.000 |
| zipcode28803 | 21.366 | 8.449 | 2.529 | 0.012 |
| zipcode28804 | 27.466 | 8.644 | 3.178 | 0.002 |
| zipcode28805 | 14.894 | 8.684 | 1.715 | 0.087 |
| zipcode28806 | 2.323 | 7.862 | 0.296 | 0.768 |
| zipcode28815 | 34.707 | 61.244 | 0.567 | 0.571 |
| zipcode29710 | -6.194 | 61.439 | -0.101 | 0.920 |
| room_typePrivate room | -18.525 | 3.976 | -4.659 | 0.000 |
| room_typeShared room | -81.884 | 23.785 | -3.443 | 0.001 |
| accommodates | 12.651 | 1.041 | 12.152 | 0.000 |
| bathrooms | 44.178 | 3.799 | 11.628 | 0.000 |
| cleaning_fee | 0.311 | 0.046 | 6.784 | 0.000 |
| minimum_nights | -1.921 | 0.208 | -9.227 | 0.000 |
| availability_30 | 0.462 | 0.201 | 2.295 | 0.022 |
| review_scores_cleanliness | 13.436 | 3.794 | 3.542 | 0.000 |
| review_scores_checkin | -13.548 | 4.825 | -2.808 | 0.005 |
| review_scores_location | 5.638 | 4.049 | 1.392 | 0.164 |
| review_scores_value | -7.784 | 3.938 | -1.977 | 0.048 |
| reviews_per_month | -4.461 | 0.697 | -6.403 | 0.000 |
| cancellation_policymoderate | 3.310 | 4.287 | 0.772 | 0.440 |
| cancellation_policystrict_14_with_grace_period | 12.669 | 4.680 | 2.707 | 0.007 |
| cancellation_policysuper_strict_30 | 8.309 | 15.512 | 0.536 | 0.592 |
| cancellation_policysuper_strict_60 | 216.418 | 13.023 | 16.618 | 0.000 |
#model with interaction effects
interactions.model <- lm(price ~ cleaning_fee * bathrooms + cleaning_fee * accommodates + room_type * bathrooms + accommodates * bathrooms + cleaning_fee * review_scores_cleanliness + zipcode * review_scores_location + availability_30 * minimum_nights + cancellation_policy * accommodates + host_is_superhost
+ host_listings_count
+ zipcode
+ room_type
+ accommodates
+ bathrooms
+ beds
+ bed_type
+ cleaning_fee
+ extra_people
+ minimum_nights
+ availability_30
+ number_of_reviews
+ review_scores_rating
+ review_scores_accuracy
+ review_scores_cleanliness
+ review_scores_checkin
+ review_scores_communication
+ review_scores_location
+ review_scores_value
+ reviews_per_month
+ cancellation_policy, data=train.airbnb)
#anova test
kable(anova(full.model, interactions.model))| Res.Df | RSS | Df | Sum of Sq | F | Pr(>F) |
|---|---|---|---|---|---|
| 1480 | 5373756 | NA | NA | NA | NA |
| 1462 | 4920903 | 18 | 452852.8 | 7.474586 | 0 |
backwards.model.2 <- ols_step_backward_aic(interactions.model, details=TRUE)## Backward Elimination Method
## ---------------------------
##
## Candidate Terms:
##
## 1 . cleaning_fee
## 2 . bathrooms
## 3 . accommodates
## 4 . room_type
## 5 . review_scores_cleanliness
## 6 . zipcode
## 7 . review_scores_location
## 8 . availability_30
## 9 . minimum_nights
## 10 . cancellation_policy
## 11 . host_is_superhost
## 12 . host_listings_count
## 13 . beds
## 14 . bed_type
## 15 . extra_people
## 16 . number_of_reviews
## 17 . review_scores_rating
## 18 . review_scores_accuracy
## 19 . review_scores_checkin
## 20 . review_scores_communication
## 21 . review_scores_value
## 22 . reviews_per_month
## 23 . cleaning_fee:bathrooms
## 24 . cleaning_fee:accommodates
## 25 . bathrooms:room_type
## 26 . bathrooms:accommodates
## 27 . cleaning_fee:review_scores_cleanliness
## 28 . zipcode:review_scores_location
## 29 . availability_30:minimum_nights
## 30 . accommodates:cancellation_policy
##
## Step 0: AIC = 16725.03
## price ~ cleaning_fee + bathrooms + accommodates + room_type + review_scores_cleanliness + zipcode + review_scores_location + availability_30 + minimum_nights + cancellation_policy + host_is_superhost + host_listings_count + beds + bed_type + extra_people + number_of_reviews + review_scores_rating + review_scores_accuracy + review_scores_checkin + review_scores_communication + review_scores_value + reviews_per_month + cleaning_fee:bathrooms + cleaning_fee:accommodates + bathrooms:room_type + bathrooms:accommodates + cleaning_fee:review_scores_cleanliness + zipcode:review_scores_location + availability_30:minimum_nights + accommodates:cancellation_policy
##
## ------------------------------------------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## ------------------------------------------------------------------------------------------------------------
## review_scores_location 1 16725.029 0.000 4920903.151 0.714 0.703
## review_scores_rating 1 16723.030 3.478 4920906.629 0.714 0.703
## beds 1 16723.069 129.051 4921032.202 0.714 0.703
## review_scores_accuracy 1 16723.070 132.798 4921035.949 0.714 0.703
## host_listings_count 1 16723.137 349.056 4921252.207 0.714 0.703
## review_scores_communication 1 16723.226 636.520 4921539.671 0.714 0.703
## extra_people 1 16723.649 2006.550 4922909.701 0.714 0.703
## accommodates 1 16723.882 2760.120 4923663.271 0.714 0.703
## number_of_reviews 1 16723.966 3033.483 4923936.634 0.714 0.703
## cleaning_fee:bathrooms 1 16724.076 3389.448 4924292.598 0.714 0.703
## host_is_superhost 1 16724.355 4292.235 4925195.386 0.714 0.703
## availability_30:minimum_nights 1 16724.358 4303.918 4925207.069 0.714 0.703
## cleaning_fee:accommodates 1 16724.663 5291.917 4926195.068 0.714 0.703
## review_scores_checkin 1 16724.859 5926.783 4926829.934 0.714 0.703
## room_type 1 16722.962 6260.770 4927163.920 0.714 0.703
## bathrooms:room_type 1 16723.006 6402.976 4927306.127 0.714 0.703
## bed_type 1 16719.329 7451.048 4928354.199 0.714 0.704
## bathrooms 1 16725.552 8171.861 4929075.012 0.714 0.703
## review_scores_value 1 16725.831 9077.318 4929980.469 0.714 0.703
## availability_30 1 16726.803 12231.641 4933134.791 0.714 0.703
## cleaning_fee:review_scores_cleanliness 1 16732.978 32314.710 4953217.861 0.712 0.701
## cleaning_fee 1 16734.603 37612.341 4958515.492 0.712 0.701
## cancellation_policy 1 16729.802 41525.536 4962428.686 0.712 0.701
## review_scores_cleanliness 1 16736.338 43276.260 4964179.410 0.712 0.701
## bathrooms:accommodates 1 16738.645 50813.514 4971716.664 0.711 0.700
## zipcode:review_scores_location 1 16729.919 87829.147 5008732.297 0.709 0.699
## zipcode 1 16731.535 93155.860 5014059.011 0.709 0.699
## reviews_per_month 1 16765.245 138586.048 5059489.199 0.706 0.695
## accommodates:cancellation_policy 1 16761.517 146154.290 5067057.441 0.706 0.695
## minimum_nights 1 16774.474 169399.693 5090302.844 0.704 0.693
## ------------------------------------------------------------------------------------------------------------
##
##
## - bed_type
##
##
## Step 1 : AIC = 16719.33
## price ~ cleaning_fee + bathrooms + accommodates + room_type + review_scores_cleanliness + zipcode + review_scores_location + availability_30 + minimum_nights + cancellation_policy + host_is_superhost + host_listings_count + beds + extra_people + number_of_reviews + review_scores_rating + review_scores_accuracy + review_scores_checkin + review_scores_communication + review_scores_value + reviews_per_month + cleaning_fee:bathrooms + cleaning_fee:accommodates + bathrooms:room_type + bathrooms:accommodates + cleaning_fee:review_scores_cleanliness + zipcode:review_scores_location + availability_30:minimum_nights + accommodates:cancellation_policy
##
## ------------------------------------------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## ------------------------------------------------------------------------------------------------------------
## review_scores_location 1 16719.329 0.000 4928354.199 0.714 0.704
## review_scores_rating 1 16717.331 4.844 4928359.043 0.714 0.704
## beds 1 16717.363 109.083 4928463.282 0.714 0.704
## review_scores_accuracy 1 16717.392 204.763 4928558.961 0.714 0.704
## host_listings_count 1 16717.428 320.589 4928674.788 0.714 0.704
## review_scores_communication 1 16717.518 612.105 4928966.304 0.714 0.704
## extra_people 1 16717.955 2029.507 4930383.706 0.714 0.704
## accommodates 1 16718.259 3015.143 4931369.342 0.714 0.704
## number_of_reviews 1 16718.288 3108.441 4931462.640 0.714 0.704
## cleaning_fee:bathrooms 1 16718.328 3238.549 4931592.747 0.714 0.704
## host_is_superhost 1 16718.655 4301.136 4932655.334 0.714 0.703
## availability_30:minimum_nights 1 16718.757 4630.369 4932984.568 0.714 0.703
## cleaning_fee:accommodates 1 16718.975 5338.652 4933692.851 0.714 0.703
## review_scores_checkin 1 16719.099 5740.974 4934095.173 0.714 0.703
## bathrooms:room_type 1 16717.255 6249.655 4934603.854 0.714 0.704
## room_type 1 16717.302 6401.776 4934755.975 0.714 0.704
## bathrooms 1 16719.776 7939.746 4936293.945 0.713 0.703
## review_scores_value 1 16720.080 8925.616 4937279.815 0.713 0.703
## availability_30 1 16721.183 12512.728 4940866.927 0.713 0.703
## cleaning_fee:review_scores_cleanliness 1 16727.438 32885.905 4961240.103 0.712 0.702
## cleaning_fee 1 16729.250 38804.770 4967158.969 0.712 0.701
## cancellation_policy 1 16724.007 41278.905 4969633.104 0.711 0.702
## review_scores_cleanliness 1 16730.672 43451.771 4971805.969 0.711 0.701
## bathrooms:accommodates 1 16733.086 51355.263 4979709.462 0.711 0.701
## zipcode:review_scores_location 1 16724.341 88364.708 5016718.907 0.709 0.700
## zipcode 1 16725.510 92224.786 5020578.984 0.709 0.700
## reviews_per_month 1 16759.714 139358.949 5067713.148 0.706 0.695
## accommodates:cancellation_policy 1 16755.188 144277.909 5072632.108 0.705 0.696
## minimum_nights 1 16768.563 168950.160 5097304.359 0.704 0.694
## ------------------------------------------------------------------------------------------------------------
##
## - bathrooms:room_type
##
##
## Step 2 : AIC = 16717.26
## price ~ cleaning_fee + bathrooms + accommodates + room_type + review_scores_cleanliness + zipcode + review_scores_location + availability_30 + minimum_nights + cancellation_policy + host_is_superhost + host_listings_count + beds + extra_people + number_of_reviews + review_scores_rating + review_scores_accuracy + review_scores_checkin + review_scores_communication + review_scores_value + reviews_per_month + cleaning_fee:bathrooms + cleaning_fee:accommodates + bathrooms:accommodates + cleaning_fee:review_scores_cleanliness + zipcode:review_scores_location + availability_30:minimum_nights + accommodates:cancellation_policy
##
## ------------------------------------------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## ------------------------------------------------------------------------------------------------------------
## review_scores_location 1 16717.255 0.000 4934603.854 0.714 0.704
## review_scores_rating 1 16715.256 3.075 4934606.929 0.714 0.704
## beds 1 16715.277 68.285 4934672.139 0.714 0.704
## review_scores_accuracy 1 16715.291 114.026 4934717.880 0.714 0.704
## host_listings_count 1 16715.400 468.291 4935072.145 0.713 0.704
## review_scores_communication 1 16715.430 566.528 4935170.382 0.713 0.704
## extra_people 1 16715.906 2110.710 4936714.564 0.713 0.704
## accommodates 1 16716.022 2487.703 4937091.557 0.713 0.704
## number_of_reviews 1 16716.079 2673.477 4937277.331 0.713 0.704
## bathrooms 1 16716.292 3364.618 4937968.472 0.713 0.704
## host_is_superhost 1 16716.632 4472.096 4939075.950 0.713 0.703
## availability_30:minimum_nights 1 16716.718 4751.428 4939355.282 0.713 0.703
## cleaning_fee:bathrooms 1 16716.805 5032.551 4939636.405 0.713 0.703
## review_scores_checkin 1 16717.119 6054.855 4940658.709 0.713 0.703
## review_scores_value 1 16718.015 8966.030 4943569.884 0.713 0.703
## cleaning_fee:accommodates 1 16718.018 8975.534 4943579.388 0.713 0.703
## availability_30 1 16718.637 10988.861 4945592.715 0.713 0.703
## cleaning_fee:review_scores_cleanliness 1 16724.851 31249.592 4965853.446 0.712 0.702
## cleaning_fee 1 16727.377 39509.573 4974113.427 0.711 0.701
## cancellation_policy 1 16722.058 41739.788 4976343.642 0.711 0.702
## review_scores_cleanliness 1 16728.296 42517.311 4977121.165 0.711 0.701
## bathrooms:accommodates 1 16736.453 69298.471 5003902.325 0.709 0.700
## zipcode:review_scores_location 1 16722.238 88380.203 5022984.057 0.708 0.700
## zipcode 1 16724.443 95671.653 5030275.507 0.708 0.699
## reviews_per_month 1 16758.599 142737.952 5077341.806 0.705 0.695
## accommodates:cancellation_policy 1 16752.822 143483.613 5078087.467 0.705 0.696
## room_type 1 16760.276 155033.816 5089637.670 0.705 0.695
## minimum_nights 1 16766.926 170628.472 5105232.326 0.704 0.694
## ------------------------------------------------------------------------------------------------------------
##
## - review_scores_rating
##
##
## Step 3 : AIC = 16715.26
## price ~ cleaning_fee + bathrooms + accommodates + room_type + review_scores_cleanliness + zipcode + review_scores_location + availability_30 + minimum_nights + cancellation_policy + host_is_superhost + host_listings_count + beds + extra_people + number_of_reviews + review_scores_accuracy + review_scores_checkin + review_scores_communication + review_scores_value + reviews_per_month + cleaning_fee:bathrooms + cleaning_fee:accommodates + bathrooms:accommodates + cleaning_fee:review_scores_cleanliness + zipcode:review_scores_location + availability_30:minimum_nights + accommodates:cancellation_policy
##
## ------------------------------------------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## ------------------------------------------------------------------------------------------------------------
## review_scores_location 1 16715.256 0.000 4934606.929 0.714 0.704
## beds 1 16713.278 68.432 4934675.361 0.714 0.704
## review_scores_accuracy 1 16713.291 110.952 4934717.881 0.714 0.704
## host_listings_count 1 16713.400 465.458 4935072.388 0.713 0.704
## review_scores_communication 1 16713.432 571.147 4935178.076 0.713 0.704
## extra_people 1 16713.907 2112.374 4936719.304 0.713 0.704
## accommodates 1 16714.022 2484.654 4937091.583 0.713 0.704
## number_of_reviews 1 16714.094 2719.222 4937326.151 0.713 0.704
## bathrooms 1 16714.293 3367.192 4937974.121 0.713 0.704
## host_is_superhost 1 16714.640 4495.181 4939102.110 0.713 0.704
## availability_30:minimum_nights 1 16714.724 4766.362 4939373.292 0.713 0.704
## cleaning_fee:bathrooms 1 16714.805 5030.604 4939637.533 0.713 0.704
## review_scores_checkin 1 16715.123 6064.188 4940671.118 0.713 0.704
## cleaning_fee:accommodates 1 16716.018 8974.259 4943581.188 0.713 0.703
## review_scores_value 1 16716.198 9557.271 4944164.200 0.713 0.703
## availability_30 1 16716.637 10985.799 4945592.728 0.713 0.703
## cleaning_fee:review_scores_cleanliness 1 16722.879 31338.466 4965945.395 0.712 0.702
## cleaning_fee 1 16725.439 39709.597 4974316.527 0.711 0.702
## cancellation_policy 1 16720.070 41774.174 4976381.104 0.711 0.702
## review_scores_cleanliness 1 16727.675 47031.830 4981638.759 0.711 0.701
## bathrooms:accommodates 1 16734.479 69381.296 5003988.226 0.709 0.700
## zipcode:review_scores_location 1 16720.257 88439.998 5023046.928 0.708 0.700
## zipcode 1 16722.445 95675.625 5030282.554 0.708 0.700
## reviews_per_month 1 16756.653 142915.685 5077522.615 0.705 0.695
## accommodates:cancellation_policy 1 16750.915 143792.114 5078399.044 0.705 0.696
## room_type 1 16758.310 155144.919 5089751.848 0.705 0.695
## minimum_nights 1 16765.456 172406.097 5107013.026 0.704 0.694
## ------------------------------------------------------------------------------------------------------------
##
## - beds
##
##
## Step 4 : AIC = 16713.28
## price ~ cleaning_fee + bathrooms + accommodates + room_type + review_scores_cleanliness + zipcode + review_scores_location + availability_30 + minimum_nights + cancellation_policy + host_is_superhost + host_listings_count + extra_people + number_of_reviews + review_scores_accuracy + review_scores_checkin + review_scores_communication + review_scores_value + reviews_per_month + cleaning_fee:bathrooms + cleaning_fee:accommodates + bathrooms:accommodates + cleaning_fee:review_scores_cleanliness + zipcode:review_scores_location + availability_30:minimum_nights + accommodates:cancellation_policy
##
## ------------------------------------------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## ------------------------------------------------------------------------------------------------------------
## review_scores_location 1 16713.278 0.000 4934675.361 0.714 0.704
## review_scores_accuracy 1 16711.311 108.516 4934783.877 0.713 0.704
## host_listings_count 1 16711.407 420.071 4935095.433 0.713 0.704
## review_scores_communication 1 16711.458 585.155 4935260.516 0.713 0.704
## extra_people 1 16711.923 2097.448 4936772.809 0.713 0.704
## number_of_reviews 1 16712.123 2744.849 4937420.210 0.713 0.704
## accommodates 1 16712.280 3255.068 4937930.430 0.713 0.704
## bathrooms 1 16712.324 3397.781 4938073.143 0.713 0.704
## host_is_superhost 1 16712.668 4516.119 4939191.481 0.713 0.704
## availability_30:minimum_nights 1 16712.744 4763.115 4939438.476 0.713 0.704
## cleaning_fee:bathrooms 1 16712.830 5043.928 4939719.289 0.713 0.704
## review_scores_checkin 1 16713.134 6032.310 4940707.671 0.713 0.704
## cleaning_fee:accommodates 1 16714.022 8917.630 4943592.992 0.713 0.704
## review_scores_value 1 16714.222 9567.988 4944243.350 0.713 0.704
## availability_30 1 16714.647 10949.583 4945624.944 0.713 0.704
## cleaning_fee:review_scores_cleanliness 1 16720.919 31399.668 4966075.029 0.712 0.702
## cleaning_fee 1 16723.451 39681.104 4974356.466 0.711 0.702
## cancellation_policy 1 16718.195 42114.433 4976789.794 0.711 0.702
## review_scores_cleanliness 1 16725.684 46993.084 4981668.445 0.711 0.701
## bathrooms:accommodates 1 16732.514 69428.738 5004104.099 0.709 0.700
## zipcode:review_scores_location 1 16718.358 88704.945 5023380.306 0.708 0.700
## zipcode 1 16720.602 96125.227 5030800.589 0.708 0.700
## reviews_per_month 1 16754.673 142914.439 5077589.801 0.705 0.696
## accommodates:cancellation_policy 1 16749.884 146959.128 5081634.489 0.705 0.696
## room_type 1 16756.319 155108.608 5089783.969 0.705 0.695
## minimum_nights 1 16763.549 172649.681 5107325.043 0.703 0.694
## ------------------------------------------------------------------------------------------------------------
##
## - review_scores_accuracy
##
##
## Step 5 : AIC = 16711.31
## price ~ cleaning_fee + bathrooms + accommodates + room_type + review_scores_cleanliness + zipcode + review_scores_location + availability_30 + minimum_nights + cancellation_policy + host_is_superhost + host_listings_count + extra_people + number_of_reviews + review_scores_checkin + review_scores_communication + review_scores_value + reviews_per_month + cleaning_fee:bathrooms + cleaning_fee:accommodates + bathrooms:accommodates + cleaning_fee:review_scores_cleanliness + zipcode:review_scores_location + availability_30:minimum_nights + accommodates:cancellation_policy
##
## ------------------------------------------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## ------------------------------------------------------------------------------------------------------------
## review_scores_location 1 16711.311 0.000 4934783.877 0.713 0.704
## host_listings_count 1 16709.442 423.991 4935207.868 0.713 0.704
## review_scores_communication 1 16709.561 811.925 4935595.802 0.713 0.704
## extra_people 1 16709.948 2069.643 4936853.520 0.713 0.704
## number_of_reviews 1 16710.160 2757.926 4937541.803 0.713 0.704
## accommodates 1 16710.304 3225.430 4938009.307 0.713 0.704
## bathrooms 1 16710.366 3426.112 4938209.988 0.713 0.704
## host_is_superhost 1 16710.714 4555.858 4939339.735 0.713 0.704
## availability_30:minimum_nights 1 16710.768 4731.547 4939515.424 0.713 0.704
## cleaning_fee:bathrooms 1 16710.852 5006.445 4939790.322 0.713 0.704
## review_scores_checkin 1 16711.324 6538.411 4941322.288 0.713 0.704
## cleaning_fee:accommodates 1 16712.040 8866.683 4943650.560 0.713 0.704
## review_scores_value 1 16712.415 10087.752 4944871.629 0.713 0.704
## availability_30 1 16712.711 11051.623 4945835.500 0.713 0.704
## cleaning_fee:review_scores_cleanliness 1 16718.945 31376.027 4966159.903 0.712 0.702
## cleaning_fee 1 16721.478 39659.795 4974443.672 0.711 0.702
## cancellation_policy 1 16716.200 42024.718 4976808.595 0.711 0.702
## review_scores_cleanliness 1 16724.578 49816.322 4984600.199 0.711 0.701
## bathrooms:accommodates 1 16730.540 69404.369 5004188.246 0.709 0.700
## zipcode:review_scores_location 1 16716.447 88891.199 5023675.075 0.708 0.700
## zipcode 1 16718.688 96303.339 5031087.215 0.708 0.700
## reviews_per_month 1 16752.691 142864.648 5077648.524 0.705 0.696
## accommodates:cancellation_policy 1 16748.212 147949.501 5082733.378 0.705 0.696
## room_type 1 16754.333 155046.651 5089830.528 0.704 0.695
## minimum_nights 1 16761.561 172581.481 5107365.358 0.703 0.694
## ------------------------------------------------------------------------------------------------------------
##
## - host_listings_count
##
##
## Step 6 : AIC = 16709.44
## price ~ cleaning_fee + bathrooms + accommodates + room_type + review_scores_cleanliness + zipcode + review_scores_location + availability_30 + minimum_nights + cancellation_policy + host_is_superhost + extra_people + number_of_reviews + review_scores_checkin + review_scores_communication + review_scores_value + reviews_per_month + cleaning_fee:bathrooms + cleaning_fee:accommodates + bathrooms:accommodates + cleaning_fee:review_scores_cleanliness + zipcode:review_scores_location + availability_30:minimum_nights + accommodates:cancellation_policy
##
## ------------------------------------------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## ------------------------------------------------------------------------------------------------------------
## review_scores_location 1 16709.442 0.000 4935207.868 0.713 0.704
## review_scores_communication 1 16707.736 955.252 4936163.119 0.713 0.704
## extra_people 1 16708.044 1956.957 4937164.825 0.713 0.704
## number_of_reviews 1 16708.291 2759.319 4937967.186 0.713 0.704
## accommodates 1 16708.395 3095.473 4938303.341 0.713 0.704
## bathrooms 1 16708.573 3676.392 4938884.259 0.713 0.704
## host_is_superhost 1 16708.798 4406.497 4939614.364 0.713 0.704
## cleaning_fee:bathrooms 1 16708.878 4666.521 4939874.389 0.713 0.704
## availability_30:minimum_nights 1 16708.882 4680.712 4939888.579 0.713 0.704
## review_scores_checkin 1 16709.416 6415.219 4941623.086 0.713 0.704
## cleaning_fee:accommodates 1 16710.042 8449.295 4943657.163 0.713 0.704
## review_scores_value 1 16710.520 10004.754 4945212.621 0.713 0.704
## availability_30 1 16710.856 11099.430 4946307.297 0.713 0.704
## cleaning_fee:review_scores_cleanliness 1 16718.257 35242.342 4970450.210 0.711 0.702
## cleaning_fee 1 16721.054 44396.442 4979604.309 0.711 0.702
## cancellation_policy 1 16716.122 47896.238 4983104.105 0.711 0.702
## review_scores_cleanliness 1 16722.773 50032.261 4985240.129 0.711 0.702
## bathrooms:accommodates 1 16728.560 69046.941 5004254.809 0.709 0.700
## zipcode:review_scores_location 1 16714.673 89214.523 5024422.390 0.708 0.700
## zipcode 1 16716.697 95906.845 5031114.713 0.708 0.700
## reviews_per_month 1 16750.748 142632.581 5077840.448 0.705 0.696
## accommodates:cancellation_policy 1 16746.213 147526.854 5082734.722 0.705 0.696
## room_type 1 16752.443 154989.855 5090197.723 0.704 0.695
## minimum_nights 1 16759.996 173622.063 5108829.930 0.703 0.694
## ------------------------------------------------------------------------------------------------------------
##
## - review_scores_communication
##
##
## Step 7 : AIC = 16707.74
## price ~ cleaning_fee + bathrooms + accommodates + room_type + review_scores_cleanliness + zipcode + review_scores_location + availability_30 + minimum_nights + cancellation_policy + host_is_superhost + extra_people + number_of_reviews + review_scores_checkin + review_scores_value + reviews_per_month + cleaning_fee:bathrooms + cleaning_fee:accommodates + bathrooms:accommodates + cleaning_fee:review_scores_cleanliness + zipcode:review_scores_location + availability_30:minimum_nights + accommodates:cancellation_policy
##
## ------------------------------------------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## ------------------------------------------------------------------------------------------------------------
## review_scores_location 1 16707.736 0.000 4936163.119 0.713 0.704
## extra_people 1 16706.326 1917.404 4938080.523 0.713 0.705
## number_of_reviews 1 16706.610 2841.531 4939004.650 0.713 0.705
## accommodates 1 16706.685 3082.217 4939245.337 0.713 0.704
## bathrooms 1 16706.871 3688.414 4939851.534 0.713 0.704
## host_is_superhost 1 16707.076 4353.826 4940516.945 0.713 0.704
## cleaning_fee:bathrooms 1 16707.151 4597.638 4940760.758 0.713 0.704
## availability_30:minimum_nights 1 16707.171 4662.123 4940825.243 0.713 0.704
## cleaning_fee:accommodates 1 16708.267 8226.236 4944389.355 0.713 0.704
## review_scores_value 1 16709.096 10924.378 4947087.497 0.713 0.704
## availability_30 1 16709.224 11340.328 4947503.448 0.713 0.704
## review_scores_checkin 1 16711.323 18177.539 4954340.659 0.712 0.704
## cleaning_fee:review_scores_cleanliness 1 16716.500 35081.835 4971244.955 0.711 0.703
## cleaning_fee 1 16719.253 44092.876 4980255.996 0.711 0.702
## cancellation_policy 1 16714.342 47660.843 4983823.963 0.711 0.702
## review_scores_cleanliness 1 16720.789 49128.803 4985291.922 0.711 0.702
## bathrooms:accommodates 1 16726.794 68862.513 5005025.632 0.709 0.701
## zipcode:review_scores_location 1 16712.826 88763.050 5024926.169 0.708 0.701
## zipcode 1 16714.960 95822.515 5031985.634 0.708 0.700
## reviews_per_month 1 16748.960 142383.408 5078546.527 0.705 0.696
## accommodates:cancellation_policy 1 16745.230 149975.947 5086139.067 0.705 0.696
## room_type 1 16750.648 154720.267 5090883.387 0.704 0.696
## minimum_nights 1 16758.270 173586.333 5109749.453 0.703 0.694
## ------------------------------------------------------------------------------------------------------------
##
## - extra_people
##
##
## Step 8 : AIC = 16706.33
## price ~ cleaning_fee + bathrooms + accommodates + room_type + review_scores_cleanliness + zipcode + review_scores_location + availability_30 + minimum_nights + cancellation_policy + host_is_superhost + number_of_reviews + review_scores_checkin + review_scores_value + reviews_per_month + cleaning_fee:bathrooms + cleaning_fee:accommodates + bathrooms:accommodates + cleaning_fee:review_scores_cleanliness + zipcode:review_scores_location + availability_30:minimum_nights + accommodates:cancellation_policy
##
## ------------------------------------------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## ------------------------------------------------------------------------------------------------------------
## review_scores_location 1 16706.326 0.000 4938080.523 0.713 0.705
## number_of_reviews 1 16705.154 2691.496 4940772.019 0.713 0.705
## accommodates 1 16705.335 3280.074 4941360.597 0.713 0.705
## bathrooms 1 16705.418 3549.729 4941630.252 0.713 0.705
## cleaning_fee:bathrooms 1 16705.721 4535.572 4942616.095 0.713 0.704
## host_is_superhost 1 16705.760 4661.235 4942741.758 0.713 0.704
## availability_30:minimum_nights 1 16705.801 4794.636 4942875.159 0.713 0.704
## cleaning_fee:accommodates 1 16707.028 8786.670 4946867.193 0.713 0.704
## review_scores_value 1 16707.735 11086.841 4949167.364 0.713 0.704
## availability_30 1 16707.916 11676.036 4949756.559 0.713 0.704
## review_scores_checkin 1 16709.926 18226.461 4956306.984 0.712 0.704
## cleaning_fee:review_scores_cleanliness 1 16714.948 34629.887 4972710.410 0.711 0.703
## cleaning_fee 1 16718.333 45715.741 4983796.264 0.711 0.702
## cancellation_policy 1 16712.759 47113.551 4985194.074 0.711 0.703
## review_scores_cleanliness 1 16719.323 48962.441 4987042.964 0.710 0.702
## bathrooms:accommodates 1 16725.410 68972.191 5007052.714 0.709 0.701
## zipcode:review_scores_location 1 16711.465 88959.076 5027039.599 0.708 0.701
## zipcode 1 16713.613 96067.719 5034148.242 0.708 0.700
## reviews_per_month 1 16747.951 143778.414 5081858.937 0.705 0.696
## accommodates:cancellation_policy 1 16744.019 150699.227 5088779.750 0.705 0.696
## room_type 1 16748.712 153020.114 5091100.637 0.704 0.696
## minimum_nights 1 16757.335 175249.457 5113329.980 0.703 0.694
## ------------------------------------------------------------------------------------------------------------
##
## - number_of_reviews
##
##
## Step 9 : AIC = 16705.15
## price ~ cleaning_fee + bathrooms + accommodates + room_type + review_scores_cleanliness + zipcode + review_scores_location + availability_30 + minimum_nights + cancellation_policy + host_is_superhost + review_scores_checkin + review_scores_value + reviews_per_month + cleaning_fee:bathrooms + cleaning_fee:accommodates + bathrooms:accommodates + cleaning_fee:review_scores_cleanliness + zipcode:review_scores_location + availability_30:minimum_nights + accommodates:cancellation_policy
##
## ------------------------------------------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## ------------------------------------------------------------------------------------------------------------
## review_scores_location 1 16705.154 0.000 4940772.019 0.713 0.705
## accommodates 1 16704.147 3228.415 4944000.434 0.713 0.705
## bathrooms 1 16704.270 3628.882 4944400.901 0.713 0.705
## host_is_superhost 1 16704.363 3931.356 4944703.375 0.713 0.705
## cleaning_fee:bathrooms 1 16704.570 4603.513 4945375.532 0.713 0.705
## availability_30:minimum_nights 1 16704.641 4835.635 4945607.654 0.713 0.705
## cleaning_fee:accommodates 1 16705.931 9034.802 4949806.821 0.713 0.704
## review_scores_value 1 16706.637 11333.649 4952105.668 0.712 0.704
## availability_30 1 16706.726 11623.561 4952395.580 0.712 0.704
## review_scores_checkin 1 16709.003 19049.343 4959821.362 0.712 0.704
## cleaning_fee:review_scores_cleanliness 1 16713.635 34186.803 4974958.823 0.711 0.703
## cleaning_fee 1 16717.296 46180.788 4986952.807 0.710 0.702
## cancellation_policy 1 16711.883 48107.043 4988879.062 0.710 0.703
## review_scores_cleanliness 1 16718.438 49928.982 4990701.001 0.710 0.702
## bathrooms:accommodates 1 16724.096 68541.671 5009313.690 0.709 0.701
## zipcode:review_scores_location 1 16710.061 88239.895 5029011.914 0.708 0.701
## zipcode 1 16712.395 95967.034 5036739.054 0.708 0.700
## accommodates:cancellation_policy 1 16742.736 150408.246 5091180.265 0.704 0.696
## room_type 1 16748.031 154746.032 5095518.051 0.704 0.696
## minimum_nights 1 16756.481 176413.966 5117185.986 0.703 0.694
## reviews_per_month 1 16767.916 215055.913 5155827.933 0.701 0.692
## ------------------------------------------------------------------------------------------------------------
##
## - accommodates
##
##
## Step 10 : AIC = 16704.15
## price ~ cleaning_fee + bathrooms + room_type + review_scores_cleanliness + zipcode + review_scores_location + availability_30 + minimum_nights + cancellation_policy + host_is_superhost + review_scores_checkin + review_scores_value + reviews_per_month + cleaning_fee:bathrooms + cleaning_fee:accommodates + bathrooms:accommodates + cleaning_fee:review_scores_cleanliness + zipcode:review_scores_location + availability_30:minimum_nights + accommodates:cancellation_policy
##
## ------------------------------------------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## ------------------------------------------------------------------------------------------------------------
## review_scores_location 1 16704.147 0.000 4944000.434 0.713 0.705
## cleaning_fee:bathrooms 1 16702.859 2315.105 4946315.539 0.713 0.705
## bathrooms 1 16703.019 2837.386 4946837.820 0.713 0.705
## host_is_superhost 1 16703.335 3865.174 4947865.608 0.713 0.705
## availability_30:minimum_nights 1 16703.738 5177.331 4949177.765 0.713 0.704
## cleaning_fee:accommodates 1 16704.707 8333.452 4952333.886 0.712 0.704
## review_scores_value 1 16705.352 10433.840 4954434.274 0.712 0.704
## availability_30 1 16705.731 11671.216 4955671.650 0.712 0.704
## review_scores_checkin 1 16707.770 18324.058 4962324.492 0.712 0.704
## cleaning_fee:review_scores_cleanliness 1 16712.958 35288.615 4979289.049 0.711 0.703
## review_scores_cleanliness 1 16716.825 47971.835 4991972.269 0.710 0.702
## cancellation_policy 1 16711.831 51279.177 4995279.611 0.710 0.702
## cleaning_fee 1 16720.986 61655.711 5005656.145 0.709 0.701
## zipcode:review_scores_location 1 16709.180 88713.536 5032713.970 0.708 0.701
## zipcode 1 16711.498 96394.849 5040395.283 0.707 0.700
## bathrooms:accommodates 1 16736.829 114103.333 5058103.767 0.706 0.698
## room_type 1 16751.264 169089.927 5113090.361 0.703 0.695
## accommodates:cancellation_policy 1 16749.519 176681.469 5120681.903 0.703 0.695
## minimum_nights 1 16756.532 180096.973 5124097.407 0.703 0.694
## reviews_per_month 1 16767.351 216700.214 5160700.648 0.700 0.692
## ------------------------------------------------------------------------------------------------------------
##
## - cleaning_fee:bathrooms
##
##
## Step 11 : AIC = 16702.86
## price ~ cleaning_fee + bathrooms + room_type + review_scores_cleanliness + zipcode + review_scores_location + availability_30 + minimum_nights + cancellation_policy + host_is_superhost + review_scores_checkin + review_scores_value + reviews_per_month + cleaning_fee:accommodates + bathrooms:accommodates + cleaning_fee:review_scores_cleanliness + zipcode:review_scores_location + availability_30:minimum_nights + accommodates:cancellation_policy
##
## ------------------------------------------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## ------------------------------------------------------------------------------------------------------------
## review_scores_location 1 16702.859 0.000 4946315.539 0.713 0.705
## host_is_superhost 1 16701.950 3551.563 4949867.101 0.713 0.705
## bathrooms 1 16702.378 4947.473 4951263.011 0.713 0.705
## availability_30:minimum_nights 1 16702.428 5108.157 4951423.695 0.713 0.705
## cleaning_fee:accommodates 1 16702.741 6128.874 4952444.412 0.712 0.704
## review_scores_value 1 16703.945 10053.209 4956368.748 0.712 0.704
## availability_30 1 16704.328 11303.960 4957619.498 0.712 0.704
## review_scores_checkin 1 16706.560 18586.168 4964901.707 0.712 0.704
## cleaning_fee:review_scores_cleanliness 1 16713.173 40235.951 4986551.489 0.710 0.702
## review_scores_cleanliness 1 16715.526 47960.758 4994276.296 0.710 0.702
## cancellation_policy 1 16710.020 49583.718 4995899.256 0.710 0.703
## zipcode:review_scores_location 1 16707.605 87808.106 5034123.644 0.708 0.701
## cleaning_fee 1 16729.215 93140.369 5039455.908 0.707 0.699
## zipcode 1 16710.070 95975.947 5042291.485 0.707 0.701
## bathrooms:accommodates 1 16739.396 127008.268 5073323.807 0.705 0.697
## room_type 1 16749.485 167518.238 5113833.776 0.703 0.695
## accommodates:cancellation_policy 1 16747.553 174483.318 5120798.856 0.703 0.695
## minimum_nights 1 16755.591 181351.396 5127666.934 0.702 0.694
## reviews_per_month 1 16765.683 215510.522 5161826.060 0.700 0.692
## ------------------------------------------------------------------------------------------------------------
##
## - host_is_superhost
##
##
## Step 12 : AIC = 16701.95
## price ~ cleaning_fee + bathrooms + room_type + review_scores_cleanliness + zipcode + review_scores_location + availability_30 + minimum_nights + cancellation_policy + review_scores_checkin + review_scores_value + reviews_per_month + cleaning_fee:accommodates + bathrooms:accommodates + cleaning_fee:review_scores_cleanliness + zipcode:review_scores_location + availability_30:minimum_nights + accommodates:cancellation_policy
##
## ------------------------------------------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## ------------------------------------------------------------------------------------------------------------
## review_scores_location 1 16701.950 0.000 4949867.101 0.713 0.705
## bathrooms 1 16701.372 4633.932 4954501.034 0.712 0.705
## availability_30:minimum_nights 1 16701.678 5631.475 4955498.577 0.712 0.705
## cleaning_fee:accommodates 1 16701.887 6313.049 4956180.150 0.712 0.704
## review_scores_value 1 16702.671 8870.870 4958737.971 0.712 0.704
## availability_30 1 16703.352 11092.475 4960959.576 0.712 0.704
## review_scores_checkin 1 16706.860 22553.477 4972420.578 0.711 0.704
## cleaning_fee:review_scores_cleanliness 1 16712.140 39856.302 4989723.403 0.710 0.702
## cancellation_policy 1 16709.584 51175.231 5001042.332 0.710 0.702
## review_scores_cleanliness 1 16715.803 51895.940 5001763.041 0.710 0.702
## zipcode:review_scores_location 1 16706.596 87538.183 5037405.285 0.708 0.701
## cleaning_fee 1 16728.726 94601.377 5044468.478 0.707 0.699
## zipcode 1 16709.321 96578.767 5046445.868 0.707 0.701
## bathrooms:accommodates 1 16738.631 127582.905 5077450.006 0.705 0.697
## room_type 1 16748.670 167956.887 5117823.988 0.703 0.695
## accommodates:cancellation_policy 1 16746.455 173970.112 5123837.213 0.703 0.695
## minimum_nights 1 16756.975 189228.470 5139095.571 0.702 0.694
## reviews_per_month 1 16764.278 213980.396 5163847.498 0.700 0.692
## ------------------------------------------------------------------------------------------------------------
##
## - bathrooms
##
##
## Step 13 : AIC = 16701.37
## price ~ cleaning_fee + room_type + review_scores_cleanliness + zipcode + review_scores_location + availability_30 + minimum_nights + cancellation_policy + review_scores_checkin + review_scores_value + reviews_per_month + cleaning_fee:accommodates + bathrooms:accommodates + cleaning_fee:review_scores_cleanliness + zipcode:review_scores_location + availability_30:minimum_nights + accommodates:cancellation_policy
##
## ------------------------------------------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## ------------------------------------------------------------------------------------------------------------
## review_scores_location 1 16701.372 0.000 4954501.034 0.712 0.705
## availability_30:minimum_nights 1 16701.134 5747.687 4960248.721 0.712 0.704
## review_scores_value 1 16701.914 8292.336 4962793.369 0.712 0.704
## availability_30 1 16702.789 11149.565 4965650.599 0.712 0.704
## cleaning_fee:accommodates 1 16704.866 17940.166 4972441.200 0.711 0.704
## review_scores_checkin 1 16706.381 22899.635 4977400.669 0.711 0.703
## cleaning_fee:review_scores_cleanliness 1 16711.538 39814.689 4994315.723 0.710 0.702
## review_scores_cleanliness 1 16714.918 50931.324 5005432.358 0.709 0.702
## cancellation_policy 1 16709.151 51700.137 5006201.170 0.709 0.702
## zipcode:review_scores_location 1 16706.245 88373.897 5042874.931 0.707 0.701
## zipcode 1 16708.499 95855.962 5050356.995 0.707 0.700
## cleaning_fee 1 16740.632 136328.880 5090829.913 0.704 0.697
## room_type 1 16746.870 163995.568 5118496.602 0.703 0.695
## accommodates:cancellation_policy 1 16744.528 169582.083 5124083.116 0.703 0.695
## minimum_nights 1 16756.527 189845.935 5144346.969 0.701 0.693
## reviews_per_month 1 16765.504 220316.069 5174817.102 0.700 0.692
## bathrooms:accommodates 1 16863.578 565217.336 5519718.370 0.680 0.671
## ------------------------------------------------------------------------------------------------------------
##
## - availability_30:minimum_nights
##
##
## Step 14 : AIC = 16701.13
## price ~ cleaning_fee + room_type + review_scores_cleanliness + zipcode + review_scores_location + availability_30 + minimum_nights + cancellation_policy + review_scores_checkin + review_scores_value + reviews_per_month + cleaning_fee:accommodates + bathrooms:accommodates + cleaning_fee:review_scores_cleanliness + zipcode:review_scores_location + accommodates:cancellation_policy
##
## ------------------------------------------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## ------------------------------------------------------------------------------------------------------------
## review_scores_location 1 16701.134 0.000 4960248.721 0.712 0.704
## review_scores_value 1 16701.739 8505.888 4968754.610 0.712 0.704
## cleaning_fee:accommodates 1 16704.780 18458.234 4978706.955 0.711 0.704
## review_scores_checkin 1 16706.064 22665.259 4982913.981 0.711 0.703
## availability_30 1 16707.058 25925.652 4986174.373 0.711 0.703
## cleaning_fee:review_scores_cleanliness 1 16711.190 39497.547 4999746.268 0.710 0.702
## cancellation_policy 1 16708.834 51497.542 5011746.263 0.709 0.702
## review_scores_cleanliness 1 16714.850 51551.574 5011800.295 0.709 0.702
## zipcode:review_scores_location 1 16705.633 87230.200 5047478.921 0.707 0.701
## zipcode 1 16707.896 94750.419 5054999.140 0.707 0.700
## cleaning_fee 1 16740.435 136623.750 5096872.472 0.704 0.696
## room_type 1 16746.314 163113.336 5123362.057 0.703 0.695
## accommodates:cancellation_policy 1 16743.904 168476.990 5128725.711 0.702 0.695
## reviews_per_month 1 16764.113 216644.476 5176893.197 0.699 0.692
## minimum_nights 1 16787.937 298424.390 5258673.112 0.695 0.687
## bathrooms:accommodates 1 16865.508 573757.291 5534006.012 0.679 0.670
## ------------------------------------------------------------------------------------------------------------
##
##
## No more variables to be removed.
##
## Variables Removed:
##
## - bed_type
## - bathrooms:room_type
## - review_scores_rating
## - beds
## - review_scores_accuracy
## - host_listings_count
## - review_scores_communication
## - extra_people
## - number_of_reviews
## - accommodates
## - cleaning_fee:bathrooms
## - host_is_superhost
## - bathrooms
## - availability_30:minimum_nights
##
##
## Final Model Output
## ------------------
##
## Model Summary
## ----------------------------------------------------------------
## R 0.844 RMSE 57.892
## R-Squared 0.712 Coef. Var 44.041
## Adj. R-Squared 0.704 MSE 3351.519
## Pred R-Squared -Inf MAE 38.371
## ----------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## --------------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## --------------------------------------------------------------------------
## Regression 12264095.479 39 314463.987 93.827 0.0000
## Residual 4960248.721 1480 3351.519
## Total 17224344.200 1519
## --------------------------------------------------------------------------
##
## Parameter Estimates
## --------------------------------------------------------------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## --------------------------------------------------------------------------------------------------------------------------------------------
## (Intercept) 72.158 18.691 3.861 0.000 35.495 108.822
## cleaning_fee 0.563 0.088 0.285 6.385 0.000 0.390 0.736
## room_typePrivate room -25.810 3.872 -0.110 -6.667 0.000 -33.405 -18.216
## room_typeShared room -64.031 22.566 -0.041 -2.837 0.005 -108.296 -19.766
## review_scores_cleanliness 14.334 3.655 0.377 3.922 0.000 7.165 21.503
## zipcode28715 -38.506 59.334 -0.048 -0.649 0.516 -154.893 77.881
## zipcode28732 80.321 37.599 0.092 2.136 0.033 6.569 154.073
## zipcode28748 -29.032 58.557 -0.007 -0.496 0.620 -143.896 85.832
## zipcode28787 29.228 58.912 0.007 0.496 0.620 -86.331 144.787
## zipcode28801 39.795 20.361 0.157 1.954 0.051 -0.145 79.735
## zipcode28803 71.589 21.049 0.233 3.401 0.001 30.300 112.878
## zipcode28804 15.780 23.344 0.048 0.676 0.499 -30.012 61.571
## zipcode28805 1.963 25.537 0.006 0.077 0.939 -48.130 52.056
## zipcode28806 6.664 20.486 0.029 0.325 0.745 -33.520 46.849
## zipcode28815 45.637 58.662 0.011 0.778 0.437 -69.432 160.706
## zipcode29710 7.148 60.865 0.002 0.117 0.907 -112.242 126.538
## review_scores_location 4.256 4.347 0.111 0.979 0.328 -4.271 12.783
## availability_30 0.537 0.193 0.040 2.781 0.005 0.158 0.915
## minimum_nights -1.884 0.200 -0.146 -9.436 0.000 -2.275 -1.492
## cancellation_policymoderate 2.783 6.557 0.013 0.425 0.671 -10.078 15.645
## cancellation_policystrict_14_with_grace_period -7.033 7.180 -0.031 -0.979 0.328 -21.118 7.052
## cancellation_policysuper_strict_30 -58.862 37.197 -0.061 -1.582 0.114 -131.826 14.101
## cancellation_policysuper_strict_60 76.707 25.346 0.099 3.026 0.003 26.989 126.426
## review_scores_checkin -11.797 4.537 -0.310 -2.601 0.009 -20.696 -2.899
## review_scores_value -6.006 3.770 -0.157 -1.593 0.111 -13.400 1.389
## reviews_per_month -5.277 0.656 -0.132 -8.040 0.000 -6.565 -3.990
## cleaning_fee:accommodates -0.022 0.009 -0.116 -2.347 0.019 -0.040 -0.004
## accommodates:bathrooms 6.413 0.490 0.489 13.084 0.000 5.452 7.375
## cleaning_fee:review_scores_cleanliness -0.026 0.008 -0.122 -3.433 0.001 -0.041 -0.011
## zipcode28715:review_scores_location 1.861 6.225 0.022 0.299 0.765 -10.351 14.072
## zipcode28732:review_scores_location -9.569 4.141 -0.100 -2.311 0.021 -17.691 -1.447
## zipcode28748:review_scores_location NA 2.239 0.000 0.032 0.975 NA NA
## zipcode28787:review_scores_location NA 2.329 -0.015 -2.659 0.008 NA NA
## zipcode28801:review_scores_location 0.071 2.554 0.039 0.410 0.682 -4.321 4.462
## zipcode28803:review_scores_location -6.193 2.752 0.031 0.366 0.715 -10.761 -1.625
## zipcode28804:review_scores_location 1.048 2.260 -0.018 -0.275 0.783 -3.962 6.057
## zipcode28805:review_scores_location 1.006 1.529 0.032 0.716 0.474 -4.393 6.405
## zipcode28806:review_scores_location -0.622 1.585 0.239 3.588 0.000 -5.056 3.812
## zipcode28815:review_scores_location NA 6.764 0.037 2.270 0.023 NA NA
## zipcode29710:review_scores_location NA 3.382 0.000 6.402 0.000 NA NA
## cancellation_policymoderate:accommodates 1.095 NA 0.012 NA NA -1.904 4.094
## cancellation_policystrict_14_with_grace_period:accommodates 5.688 NA -0.603 NA NA 2.578 8.798
## cancellation_policysuper_strict_30:accommodates 15.356 NA -0.372 NA NA 2.089 28.623
## cancellation_policysuper_strict_60:accommodates 21.650 NA 0.150 NA NA 15.017 28.283
## --------------------------------------------------------------------------------------------------------------------------------------------final.interactions.model <- lm(price ~ cleaning_fee * accommodates + accommodates * bathrooms + cleaning_fee * review_scores_cleanliness + zipcode * review_scores_location + cancellation_policy * accommodates + host_is_superhost
+ zipcode
+ room_type
+ accommodates
+ bathrooms
+ cleaning_fee
+ minimum_nights
+ availability_30
+ review_scores_cleanliness
+ review_scores_checkin
+ review_scores_location
+ review_scores_value
+ reviews_per_month
+ cancellation_policy, data=train.airbnb)
kable(tidy(final.interactions.model), digits=3)| term | estimate | std.error | statistic | p.value |
|---|---|---|---|---|
| (Intercept) | 61.451 | 21.132 | 2.908 | 0.004 |
| cleaning_fee | 0.503 | 0.098 | 5.140 | 0.000 |
| accommodates | 1.378 | 2.372 | 0.581 | 0.562 |
| bathrooms | 9.087 | 6.797 | 1.337 | 0.181 |
| review_scores_cleanliness | 14.170 | 3.697 | 3.832 | 0.000 |
| zipcode28715 | -35.282 | 59.369 | -0.594 | 0.552 |
| zipcode28732 | 80.679 | 37.606 | 2.145 | 0.032 |
| zipcode28748 | -29.403 | 58.563 | -0.502 | 0.616 |
| zipcode28787 | 30.147 | 58.963 | 0.511 | 0.609 |
| zipcode28801 | 40.403 | 20.439 | 1.977 | 0.048 |
| zipcode28803 | 71.606 | 21.067 | 3.399 | 0.001 |
| zipcode28804 | 14.948 | 23.368 | 0.640 | 0.522 |
| zipcode28805 | 4.086 | 25.625 | 0.159 | 0.873 |
| zipcode28806 | 6.334 | 20.500 | 0.309 | 0.757 |
| zipcode28815 | 43.110 | 58.695 | 0.734 | 0.463 |
| zipcode29710 | 8.865 | 60.917 | 0.146 | 0.884 |
| review_scores_location | 4.304 | 4.354 | 0.989 | 0.323 |
| cancellation_policymoderate | 3.091 | 8.609 | 0.359 | 0.720 |
| cancellation_policystrict_14_with_grace_period | -6.105 | 9.132 | -0.669 | 0.504 |
| cancellation_policysuper_strict_30 | -54.426 | 37.624 | -1.447 | 0.148 |
| cancellation_policysuper_strict_60 | 75.350 | 26.027 | 2.895 | 0.004 |
| host_is_superhostt | 3.844 | 3.519 | 1.092 | 0.275 |
| room_typePrivate room | -26.127 | 4.007 | -6.521 | 0.000 |
| room_typeShared room | -70.252 | 23.427 | -2.999 | 0.003 |
| minimum_nights | -1.859 | 0.201 | -9.265 | 0.000 |
| availability_30 | 0.527 | 0.193 | 2.726 | 0.006 |
| review_scores_checkin | -10.903 | 4.625 | -2.357 | 0.019 |
| review_scores_value | -6.805 | 3.803 | -1.789 | 0.074 |
| reviews_per_month | -5.370 | 0.676 | -7.940 | 0.000 |
| cleaning_fee:accommodates | -0.013 | 0.011 | -1.183 | 0.237 |
| accommodates:bathrooms | 5.278 | 0.979 | 5.393 | 0.000 |
| cleaning_fee:review_scores_cleanliness | -0.027 | 0.008 | -3.473 | 0.001 |
| zipcode28715:review_scores_location | 1.457 | 6.230 | 0.234 | 0.815 |
| zipcode28732:review_scores_location | -9.638 | 4.141 | -2.327 | 0.020 |
| zipcode28801:review_scores_location | -0.041 | 2.245 | -0.018 | 0.985 |
| zipcode28803:review_scores_location | -6.223 | 2.331 | -2.670 | 0.008 |
| zipcode28804:review_scores_location | 1.085 | 2.555 | 0.425 | 0.671 |
| zipcode28805:review_scores_location | 0.746 | 2.759 | 0.270 | 0.787 |
| zipcode28806:review_scores_location | -0.642 | 2.261 | -0.284 | 0.776 |
| accommodates:cancellation_policymoderate | 0.868 | 2.340 | 0.371 | 0.711 |
| accommodates:cancellation_policystrict_14_with_grace_period | 5.412 | 2.367 | 2.286 | 0.022 |
| accommodates:cancellation_policysuper_strict_30 | 14.608 | 6.965 | 2.097 | 0.036 |
| accommodates:cancellation_policysuper_strict_60 | 21.410 | 3.808 | 5.623 | 0.000 |
summary(final.interactions.model)$adj.r.squared## [1] 0.7044265Assumptions
train.airbnb <- train.airbnb %>% mutate(stand.resid = rstandard(final.interactions.model),
pred = predict(final.interactions.model))ggplot(data = train.airbnb, aes(x=stand.resid)) + geom_histogram()## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.## Warning: Removed 2 rows containing non-finite values (stat_bin).
qqnorm(train.airbnb$stand.resid)
p1 <- ggplot(data = train.airbnb, aes(x=pred, y=stand.resid)) + geom_point() +
labs(x="Predicted", y="Residual", title="Residuals vs Predicted",
subtitle=("final.interactions.model"))+
theme(plot.title = element_text(hjust = 0.5,size=14),
plot.subtitle=element_text(hjust=0.5,size=10))
p2 <- ggplot(data = train.airbnb, aes(x=host_is_superhost, y=stand.resid)) + geom_point() +
labs(x="Predicted", y="Residual", title="Residuals vs Superhost",
subtitle=("final.interactions.model"))+
theme(plot.title = element_text(hjust = 0.5,size=14),
plot.subtitle=element_text(hjust=0.5,size=10))
p3 <- ggplot(data = train.airbnb, aes(x=zipcode, y=stand.resid)) + geom_point() +
labs(x="Predicted", y="Residual", title="Residuals vs Zipcode",
subtitle=("final.interactions.model"))+
theme(plot.title = element_text(hjust = 0.5,size=14),
plot.subtitle=element_text(hjust=0.5,size=10))
p4 <- ggplot(data = train.airbnb, aes(x=room_type, y=stand.resid)) + geom_point() +
labs(x="Predicted", y="Residual", title="Residuals vs Room Type",
subtitle=("final.interactions.model"))+
theme(plot.title = element_text(hjust = 0.5,size=14),
plot.subtitle=element_text(hjust=0.5,size=10))
p5 <- ggplot(data = train.airbnb, aes(x=accommodates, y=stand.resid)) + geom_point() +
labs(x="Number of Guests", y="Residual", title="Residuals vs Accommodates",
subtitle=("final.interactions.model"))+
theme(plot.title = element_text(hjust = 0.5,size=14),
plot.subtitle=element_text(hjust=0.5,size=10))
p6 <- ggplot(data = train.airbnb, aes(x=bathrooms, y=stand.resid)) + geom_point() +
labs(x="Number of Bathrooms", y="Residual", title="Residuals vs Bathrooms",
subtitle=("final.interactions.model"))+
theme(plot.title = element_text(hjust = 0.5,size=14),
plot.subtitle=element_text(hjust=0.5,size=10))
p7 <- ggplot(data = train.airbnb, aes(x= cleaning_fee, y=stand.resid)) + geom_point() +
labs(x="Fee ($)", y="Residual", title="Residuals vs Cleaning Fee",
subtitle=("final.interactions.model"))+
theme(plot.title = element_text(hjust = 0.5,size=14),
plot.subtitle=element_text(hjust=0.5,size=10))
p8 <-ggplot(data = train.airbnb, aes(x=minimum_nights, y=stand.resid)) + geom_point() +
labs(x="Minimum Nights", y="Residual", title="Residuals vs Minimum_nights",
subtitle=("final.interactions.model"))+
theme(plot.title = element_text(hjust = 0.5,size=14),
plot.subtitle=element_text(hjust=0.5,size=10))
p9 <- ggplot(data = train.airbnb, aes(x=availability_30, y=stand.resid)) + geom_point() +
labs(x="Number of Available Nights in the next month", y="Residual", title="Residuals vs Availability",
subtitle=("final.interactions.model"))+
theme(plot.title = element_text(hjust = 0.5,size=14),
plot.subtitle=element_text(hjust=0.5,size=10))
p10 <- ggplot(data = train.airbnb, aes(x=review_scores_cleanliness, y=stand.resid)) + geom_point() +
labs(x="Cleanliness Review (out of 100%)", y="Residual", title="Residuals vs Cleanliness Review Scores",
subtitle=("final.interactions.model"))+
theme(plot.title = element_text(hjust = 0.5,size=14),
plot.subtitle=element_text(hjust=0.5,size=10))
p11 <- ggplot(data = train.airbnb, aes(x=review_scores_checkin, y=stand.resid)) + geom_point() +
labs(x="Check-In Review (out of 100%)", y="Residual", title="Residuals vs Check-In Review Scores",
subtitle=("final.interactions.model"))+
theme(plot.title = element_text(hjust = 0.5,size=14),
plot.subtitle=element_text(hjust=0.5,size=10))
p12 <- ggplot(data = train.airbnb, aes(x=review_scores_location, y=stand.resid)) + geom_point() +
labs(x="Location Review (out of 100%)", y="Residual", title="Residuals vs Location Review Scores",
subtitle=("final.interactions.model"))+
theme(plot.title = element_text(hjust = 0.5,size=14),
plot.subtitle=element_text(hjust=0.5,size=10))
p13 <- ggplot(data = train.airbnb, aes(x=review_scores_value, y=stand.resid)) + geom_point() +
labs(x="Value Review (out of 100%)", y="Residual", title="Residuals vs Value Review Scores",
subtitle=("final.interactions.model"))+
theme(plot.title = element_text(hjust = 0.5,size=14),
plot.subtitle=element_text(hjust=0.5,size=10))
p14 <- ggplot(data = train.airbnb, aes(x=reviews_per_month, y=stand.resid)) + geom_point() +
labs(x="Reviews per month", y="Residual", title="Residuals vs Reviews per month",
subtitle=("final.interactions.model"))+
theme(plot.title = element_text(hjust = 0.5,size=14),
plot.subtitle=element_text(hjust=0.5,size=10))
p15 <- ggplot(data = train.airbnb, aes(x=cancellation_policy, y=stand.resid)) + geom_point() +
labs(x="Cancellation Policy", y="Residual", title="Residuals vs Cancellation Policy",
subtitle=("final.interactions.model"))+
theme(plot.title = element_text(hjust = 0.5,size=14),
plot.subtitle=element_text(hjust=0.5,size=10))plot_grid(p1,p2,p3,p4)## Warning: Removed 2 rows containing missing values (geom_point).
## Warning: Removed 2 rows containing missing values (geom_point).
## Warning: Removed 2 rows containing missing values (geom_point).
## Warning: Removed 2 rows containing missing values (geom_point).
plot_grid(p5,p6,p7,p8)## Warning: Removed 2 rows containing missing values (geom_point).
## Warning: Removed 2 rows containing missing values (geom_point).
## Warning: Removed 2 rows containing missing values (geom_point).
## Warning: Removed 2 rows containing missing values (geom_point).
plot_grid(p9,p10,p11,p12)## Warning: Removed 2 rows containing missing values (geom_point).
## Warning: Removed 2 rows containing missing values (geom_point).
## Warning: Removed 2 rows containing missing values (geom_point).
## Warning: Removed 2 rows containing missing values (geom_point).
plot_grid(p13,p14,p15)## Warning: Removed 2 rows containing missing values (geom_point).
## Warning: Removed 2 rows containing missing values (geom_point).
## Warning: Removed 2 rows containing missing values (geom_point).
plots - log cleaning fee
Constant variance
Normality
Independence
Leverage Points/ outliers
train.airbnb <- train.airbnb %>%
mutate(leverage = hatvalues(final.interactions.model),
cooks = cooks.distance(final.interactions.model),
obs.num = row_number())
ggplot(data=train.airbnb, aes(x=obs.num,y=leverage)) +
geom_point(alpha=0.5) +
geom_hline(yintercept=0.,color="red")+
labs(x="Observation Number",y="Leverage",title="Leverage")
ggplot(data=train.airbnb, aes(x=obs.num,y=cooks)) +
geom_point() +
geom_hline(yintercept=1,color="red")+
labs(x="Observation Number",y="Cook's Distance",title="Cook's Distance")## Warning: Removed 2 rows containing missing values (geom_point).
Prediction
#Predict on the testing set using our final model
test.predict <- predict(final.interactions.model, test.airbnb)
test.predict## 7 10 11 14 15 17
## 84.64052 72.96663 102.72190 78.52439 89.19559 117.61594
## 24 55 57 61 71 77
## 141.15764 100.28196 70.92001 224.60673 79.85453 106.31731
## 84 87 89 90 93 104
## 71.59174 302.03480 90.10250 97.18453 99.08798 64.56191
## 111 128 130 138 142 143
## 63.94932 191.76197 116.01474 241.35576 83.67427 92.82605
## 146 149 156 157 159 164
## 116.78299 208.14729 29.03607 130.48794 131.96472 96.55231
## 166 168 177 180 181 182
## 321.77135 169.97883 133.93311 54.22461 171.37529 123.24628
## 187 188 195 196 199 202
## 83.13879 129.41183 96.90332 91.73163 107.26555 137.12288
## 204 214 215 216 217 220
## 71.82477 120.39849 276.16711 78.20739 90.64574 225.68201
## 228 231 233 239 260 268
## 101.49181 74.62224 122.68531 87.03995 70.66253 95.91687
## 273 290 293 295 301 306
## 86.05838 64.83063 92.62470 108.08154 95.14538 132.09267
## 309 312 316 319 324 326
## 69.90011 89.93865 70.27217 87.88358 60.84089 116.65538
## 334 338 346 353 354 365
## 95.25934 77.80644 80.90395 171.48064 103.46610 58.36418
## 369 378 384 387 394 396
## 64.31004 141.30848 227.13629 67.63267 209.16643 120.36850
## 401 404 407 412 422 424
## 62.92323 33.90318 83.40873 134.75908 105.34516 128.93890
## 426 433 447 450 454 458
## 136.50455 42.16275 199.96111 115.05603 219.41021 135.58990
## 460 461 482 483 484 492
## 95.03399 123.77645 211.99139 100.20501 178.80776 89.10496
## 493 497 500 508 512 518
## 273.77523 163.64672 71.04001 50.73351 129.65041 109.74796
## 531 541 547 560 561 563
## 76.82616 145.36560 196.41867 86.10256 140.93783 86.02805
## 567 568 577 578 591 595
## 173.28485 132.05294 194.27134 163.73483 88.87943 40.22509
## 604 612 613 617 631 640
## 171.16731 128.47950 117.40654 90.21837 110.75231 135.71472
## 647 649 651 664 670 671
## 156.83681 59.79595 108.53126 107.51490 108.21864 332.88143
## 678 681 689 690 692 700
## 155.65743 156.14516 103.67694 97.34390 116.12719 104.94929
## 702 713 717 724 728 731
## 140.75709 79.45901 149.76556 51.54717 94.99855 183.49013
## 732 736 742 743 761 764
## 149.09961 83.75986 126.04775 58.61166 193.95938 143.61859
## 776 777 778 781 794 800
## 59.41710 205.17372 147.35860 95.99342 354.90793 97.89456
## 808 810 819 825 826 832
## 170.69947 59.32438 53.75622 60.38406 1291.68477 355.83536
## 833 835 843 846 848 852
## 826.93616 610.24315 26.91883 124.32266 143.49292 108.83741
## 855 857 860 861 863 872
## 89.84914 266.97167 199.13793 109.14788 96.09790 143.64021
## 873 875 877 881 883 902
## 86.12498 90.87021 105.69155 191.64540 76.14289 196.62050
## 905 918 926 934 941 954
## 378.75351 125.03931 58.39207 102.91001 118.03705 94.87281
## 957 962 967 968 976 985
## 135.76017 73.19486 155.78060 92.65644 61.89308 52.98880
## 996 997 999 1003 1004 1006
## 107.85574 146.63354 96.61649 75.78195 171.06713 150.37027
## 1012 1014 1023 1025 1033 1038
## 88.43676 239.25412 144.33841 130.77156 113.50738 121.20226
## 1041 1045 1054 1057 1065 1066
## 127.55646 183.09697 56.37037 58.83709 100.10278 199.46504
## 1073 1079 1086 1095 1096 1101
## 63.22049 110.55147 119.21605 200.76808 105.03937 83.67371
## 1109 1113 1114 1118 1125 1127
## 158.23133 103.28347 402.71484 44.70723 126.42077 121.58268
## 1131 1136 1137 1139 1158 1160
## 70.96992 149.30354 93.79841 85.06672 284.03715 219.19036
## 1164 1167 1168 1181 1183 1190
## 95.31415 111.68987 54.94526 114.51867 85.85812 167.48953
## 1197 1204 1210 1212 1216 1231
## 118.39270 61.61760 126.38238 121.66276 223.28282 68.68112
## 1240 1248 1249 1251 1253 1256
## 132.81735 144.93602 122.06857 121.94349 100.49788 86.16948
## 1257 1262 1267 1274 1277 1283
## 57.04636 478.38258 119.02355 142.79454 173.21395 125.60977
## 1285 1291 1295 1299 1312 1315
## 71.88676 116.70462 82.80134 28.08041 141.91871 151.41953
## 1316 1321 1323 1324 1330 1333
## 155.74949 133.84965 159.86290 53.44670 41.74258 139.42622
## 1355 1358 1370 1371 1373 1379
## 54.36748 120.29005 84.17785 116.48461 57.58637 123.15114
## 1380 1387 1388 1397 1401 1416
## 342.51711 33.85530 298.47823 132.05739 140.68136 85.48464
## 1419 1421 1422 1423 1426 1429
## 94.10036 94.04032 83.23148 132.35771 213.10800 162.59183
## 1440 1446 1450 1461 1470 1471
## 232.04987 95.76610 58.36679 118.91689 88.36015 115.91342
## 1473 1483 1490 1492 1494 1497
## 231.45314 154.49012 115.68984 87.08570 124.12264 71.48686
## 1498 1501 1502 1507 1516 1518
## 109.43765 101.12543 830.01885 109.35934 85.88425 96.67278
## 1519 1523 1529 1530 1536 1537
## 188.55252 152.21343 98.99996 166.86243 123.94426 64.85362
## 1540 1542 1547 1548 1552 1555
## 235.52346 128.23102 98.99846 25.19179 98.36552 69.49994
## 1571 1581 1588 1589 1590 1591
## 134.78513 93.90992 87.69848 218.56372 146.95380 100.77579
## 1596 1599 1608 1615 1631 1632
## 60.03465 170.91253 107.35875 126.14031 95.73617 77.05347
## 1633 1646 1649 1653 1655 1660
## 68.49891 70.57940 330.32876 44.75119 82.17580 154.36102
## 1663 1664 1672 1674 1677 1679
## 95.86411 385.88675 90.05177 89.79365 124.54784 88.17013
## 1680 1687 1706 1707 1721 1726
## 19.96967 105.27390 46.98837 77.31393 98.20966 67.11996
## 1728 1730 1733 1734 1740 1744
## 217.96603 22.55754 161.96057 81.58878 160.25164 70.01736
## 1756 1758 1759 1763 1765 1767
## 81.01858 200.62860 158.40415 87.58774 148.12821 290.94031
## 1770 1772 1779 1781 1784 1794
## 114.86574 213.42622 141.22991 43.01172 204.59672 113.03789
## 1799 1807 1808 1813 1816 1840
## 362.42630 362.15354 94.45507 86.71005 341.44847 47.45854
## 1847 1853 1856 1858 1859 1861
## 133.33555 187.29630 130.62448 153.53141 85.95288 161.38745
## 1890 1891 1897 1898 1899 1902
## 120.23151 230.45598 127.25131 318.98920 122.65381 312.37067
## 1905 1906 1912 1919 1921 1925
## 62.40026 76.41238 235.64398 209.53952 380.01928 148.03732
## 1930 1932
## 110.34180 105.30184